Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-07T05:36:57.289953Z
Paper Citation Record · LEDGER
Codimension-Two Spacelike Submanifolds with Umbilical Lightlike Normal Sections and Their Relationship to Lightlike Hypersurfaces
As of 8 August 2026, this Paper Citation Record lists 41 of 41 outbound references and 0 inbound Pith citation observations for arXiv:2506.07934.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
Reference resolution
41 of 41 outbound references displayed
- verified exact0
- verified fuzzy25
- unresolved16
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation b8774e86-6e25-445f-9548-a850b416afc5 · outbound
This paper cites an unresolved cited work.
Codimension-Two Spacelike Submanifolds with Umbilical Lightlike Normal Sections and Their Relationship to Lightlike Hypersurfaces Unresolved cited work
Reference 1
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T05:36:57.869134Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 79a97b0d-18a9-4a6e-b053-15f4972c5f16 · outbound
This paper cites J., Romero A.
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:36:57.858426Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation ddb1b913-cfdc-463b-82c7-9b1e2651f38c · outbound
This paper cites and Singer I.
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:36:57.846449Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation d80caa09-8855-4d57-be2b-9ca88cc9a081 · outbound
This paper cites K., Ehrlich P.
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:36:57.834813Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 55fd2b0b-e04e-49ff-8f21-d81d94cd6e4a · outbound
This paper cites an unresolved cited work.
Codimension-Two Spacelike Submanifolds with Umbilical Lightlike Normal Sections and Their Relationship to Lightlike Hypersurfaces Unresolved cited work
Reference 5
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T05:36:57.823348Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation dd9cb8b6-651e-44ac-8ec3-5071a527b9a2 · outbound
This paper cites L., Fern ´andez M.
Codimension-Two Spacelike Submanifolds with Umbilical Lightlike Normal Sections and Their Relationship to Lightlike Hypersurfaces L., Fern ´andez M
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:36:57.812527Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 03a98e0b-84d7-44a5-93d8-28b3b0422e4d · outbound
This paper cites L., Fern ´andez M.
Codimension-Two Spacelike Submanifolds with Umbilical Lightlike Normal Sections and Their Relationship to Lightlike Hypersurfaces L., Fern ´andez M
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:36:57.802773Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation a6125ba9-70be-4f80-9600-7a16dcb07969 · outbound
This paper cites L., Fern ´andez M.
Codimension-Two Spacelike Submanifolds with Umbilical Lightlike Normal Sections and Their Relationship to Lightlike Hypersurfaces L., Fern ´andez M
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:36:57.791844Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 61cf449a-9a24-49dc-9845-e2c3d772b6ca · outbound
This paper cites L., Palomo F.
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:36:57.781094Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 1cd4db26-eaaf-4e15-ace3-fe185324ec9e · outbound
This paper cites Y., Some conformal invariants of submanifolds and their applications,Boll.
Codimension-Two Spacelike Submanifolds with Umbilical Lightlike Normal Sections and Their Relationship to Lightlike Hypersurfaces Y., Some conformal invariants of submanifolds and their applications,Boll
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:36:57.770472Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation d27ee81b-6b8b-4da2-aac9-11febfa1fcd7 · outbound
This paper cites an unresolved cited work.
Codimension-Two Spacelike Submanifolds with Umbilical Lightlike Normal Sections and Their Relationship to Lightlike Hypersurfaces Unresolved cited work
Reference 11
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T05:36:57.758648Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 32aaf423-2f8f-45c1-8d12-e43223115c42 · outbound
This paper cites an unresolved cited work.
Codimension-Two Spacelike Submanifolds with Umbilical Lightlike Normal Sections and Their Relationship to Lightlike Hypersurfaces Unresolved cited work
Reference 12
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T05:36:57.747537Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 6bb15196-81b6-402f-bde8-b7c812343dbd · outbound
This paper cites an unresolved cited work.
Codimension-Two Spacelike Submanifolds with Umbilical Lightlike Normal Sections and Their Relationship to Lightlike Hypersurfaces Unresolved cited work
Reference 13
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T05:36:57.736366Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 43382b95-a160-426f-86da-2fd1ca99e397 · outbound
This paper cites an unresolved cited work.
Codimension-Two Spacelike Submanifolds with Umbilical Lightlike Normal Sections and Their Relationship to Lightlike Hypersurfaces Unresolved cited work
Reference 14
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T05:36:57.726186Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation a77d01fd-84a6-4fb3-b3d2-2c0571b8eada · outbound
This paper cites and Sharma R., Symmetries of Spacetimes and Riemannian Manifolds, Math.
Codimension-Two Spacelike Submanifolds with Umbilical Lightlike Normal Sections and Their Relationship to Lightlike Hypersurfaces and Sharma R., Symmetries of Spacetimes and Riemannian Manifolds, Math
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:36:57.714947Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 0fa3da91-a60f-47a0-8851-52490ef23619 · outbound
This paper cites an unresolved cited work.
Codimension-Two Spacelike Submanifolds with Umbilical Lightlike Normal Sections and Their Relationship to Lightlike Hypersurfaces Unresolved cited work
Reference 16
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T05:36:57.703638Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 6afc195e-af3d-4b51-9b86-fb3b5b9c7796 · outbound
This paper cites and Alonso-Serrano A., Observing other universe through ringholes and Klein Bottle Holes, Phys.
Codimension-Two Spacelike Submanifolds with Umbilical Lightlike Normal Sections and Their Relationship to Lightlike Hypersurfaces and Alonso-Serrano A., Observing other universe through ringholes and Klein Bottle Holes, Phys
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:36:57.693111Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 543b8f7a-5f9f-4740-bd37-5ac3a93f6c12 · outbound
This paper cites and Olea B., Totally umbilic null hypersurfaces in generalized Robertson-Walker spaces.
Codimension-Two Spacelike Submanifolds with Umbilical Lightlike Normal Sections and Their Relationship to Lightlike Hypersurfaces and Olea B., Totally umbilic null hypersurfaces in generalized Robertson-Walker spaces
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:36:57.682366Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation a6c4b8fd-035b-4514-9a84-4a08aa8398d7 · outbound
This paper cites and Olea B., Codimension two spacelike submanifolds through a null hypersurface in a lorentzian manifold, Bull.
Codimension-Two Spacelike Submanifolds with Umbilical Lightlike Normal Sections and Their Relationship to Lightlike Hypersurfaces and Olea B., Codimension two spacelike submanifolds through a null hypersurface in a lorentzian manifold, Bull
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:36:57.671025Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 31f3e908-f3c9-4a66-958c-2ddd55227f38 · outbound
This paper cites an unresolved cited work.
Codimension-Two Spacelike Submanifolds with Umbilical Lightlike Normal Sections and Their Relationship to Lightlike Hypersurfaces Unresolved cited work
Reference 20
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T05:36:57.660142Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation a4e60391-8797-4e3d-82db-a0b54ef7bd5d · outbound
This paper cites D., Compact Manifolds with Special Holonomy , Oxford Math.
Codimension-Two Spacelike Submanifolds with Umbilical Lightlike Normal Sections and Their Relationship to Lightlike Hypersurfaces D., Compact Manifolds with Special Holonomy , Oxford Math
Reference 21
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:36:57.649115Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 86ba1cdc-5422-4b1d-b5e6-c2a842a9a064 · outbound
This paper cites and Nomizu K., Foundations of Differential Geometry, Inter.
Codimension-Two Spacelike Submanifolds with Umbilical Lightlike Normal Sections and Their Relationship to Lightlike Hypersurfaces and Nomizu K., Foundations of Differential Geometry, Inter
Reference 22
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:36:57.637784Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 817d3047-64e5-491a-bef5-35fd2ef62b83 · outbound
This paper cites an unresolved cited work.
Codimension-Two Spacelike Submanifolds with Umbilical Lightlike Normal Sections and Their Relationship to Lightlike Hypersurfaces Unresolved cited work
Reference 23
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T05:36:57.626056Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 52070e42-7561-4b5f-b863-61ea00b12b9a · outbound
This paper cites N., On Null Hypersurfaces and Spacelike Surfaces in Spacetimes , Ph.D.
Codimension-Two Spacelike Submanifolds with Umbilical Lightlike Normal Sections and Their Relationship to Lightlike Hypersurfaces N., On Null Hypersurfaces and Spacelike Surfaces in Spacetimes , Ph.D
Reference 24
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:36:57.612473Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation a30353d5-7246-445e-8d0c-5c8f148e1e61 · outbound
This paper cites N., Curvature and closed trapped surfaces 4-dimensional space-times,Gen.
Codimension-Two Spacelike Submanifolds with Umbilical Lightlike Normal Sections and Their Relationship to Lightlike Hypersurfaces N., Curvature and closed trapped surfaces 4-dimensional space-times,Gen
Reference 25
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:36:57.601080Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation c37e67e6-684b-4224-a32d-bd4c4fa26036 · outbound
This paper cites N., On null submanifolds in spacetimes, Geom.
Codimension-Two Spacelike Submanifolds with Umbilical Lightlike Normal Sections and Their Relationship to Lightlike Hypersurfaces N., On null submanifolds in spacetimes, Geom
Reference 26
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:36:57.490403Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation fea5b91d-81bf-4841-9403-d7ad61d58e89 · outbound
This paper cites M., Introduction to Smooth Manifolds, Grad.
Codimension-Two Spacelike Submanifolds with Umbilical Lightlike Normal Sections and Their Relationship to Lightlike Hypersurfaces M., Introduction to Smooth Manifolds, Grad
Reference 27
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:36:57.479198Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 928d81f6-72c3-4446-9d47-e2fb3b3270fd · outbound
This paper cites and S ´anchez M., The causal hierarchy of spacetimes, in Recent developments in pseudo-Riemannian geometry, ESI Lect.
Codimension-Two Spacelike Submanifolds with Umbilical Lightlike Normal Sections and Their Relationship to Lightlike Hypersurfaces and S ´anchez M., The causal hierarchy of spacetimes, in Recent developments in pseudo-Riemannian geometry, ESI Lect
Reference 28
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:36:57.468215Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation f5406668-262b-4d66-8eeb-eb65d21d4188 · outbound
This paper cites and Palomo F.
Reference 29
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:36:57.456752Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 7e5f18b5-695f-4c20-884b-7a21602dbf1b · outbound
This paper cites an unresolved cited work.
Codimension-Two Spacelike Submanifolds with Umbilical Lightlike Normal Sections and Their Relationship to Lightlike Hypersurfaces Unresolved cited work
Reference 30
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T05:36:57.446407Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 3880009c-5cfe-42dd-a9dd-56dae2188f9b · outbound
This paper cites Press, New York, 1983.
Codimension-Two Spacelike Submanifolds with Umbilical Lightlike Normal Sections and Their Relationship to Lightlike Hypersurfaces Press, New York, 1983
Reference 31
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:36:57.436012Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation a7b78fa2-a1e7-4027-9872-89b181aaa6c5 · outbound
This paper cites an unresolved cited work.
Codimension-Two Spacelike Submanifolds with Umbilical Lightlike Normal Sections and Their Relationship to Lightlike Hypersurfaces Unresolved cited work
Reference 32
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T05:36:57.424951Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 5d258c83-8302-470a-855a-ce297ee5b849 · outbound
This paper cites and Romero A., New characterizations of compact totally umbilical spacelike surfaces in 4-dimensional Lorentz–Minkowski spacetime through a lightcone, Mediterr.
Codimension-Two Spacelike Submanifolds with Umbilical Lightlike Normal Sections and Their Relationship to Lightlike Hypersurfaces and Romero A., New characterizations of compact totally umbilical spacelike surfaces in 4-dimensional Lorentz–Minkowski spacetime through a lightcone, Mediterr
Reference 33
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:36:57.414423Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 851645a2-fc5c-460c-8de1-1ac81140ba7b · outbound
This paper cites an unresolved cited work.
Codimension-Two Spacelike Submanifolds with Umbilical Lightlike Normal Sections and Their Relationship to Lightlike Hypersurfaces Unresolved cited work
Reference 34
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T05:36:57.403668Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation d1bbc8d9-a413-4ff9-a0cb-01d56a97dfed · outbound
This paper cites an unresolved cited work.
Codimension-Two Spacelike Submanifolds with Umbilical Lightlike Normal Sections and Their Relationship to Lightlike Hypersurfaces Unresolved cited work
Reference 35
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T05:36:57.393285Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 571c3f32-d48c-4c22-a50e-a2d0bfc5e049 · outbound
This paper cites an unresolved cited work.
Codimension-Two Spacelike Submanifolds with Umbilical Lightlike Normal Sections and Their Relationship to Lightlike Hypersurfaces Unresolved cited work
Reference 36
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T05:36:57.382431Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 3db6544b-1cec-4bc8-947b-83ab5206b1cb · outbound
This paper cites Analys., 63 (2005), 511–518.
Codimension-Two Spacelike Submanifolds with Umbilical Lightlike Normal Sections and Their Relationship to Lightlike Hypersurfaces Analys., 63 (2005), 511–518
Reference 37
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:36:57.370216Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 7fed8443-bfba-47c2-8145-e4adffcd4e29 · outbound
This paper cites A., Differential Geometric Structures, McGraw-Hill, New York, 1981.
Codimension-Two Spacelike Submanifolds with Umbilical Lightlike Normal Sections and Their Relationship to Lightlike Hypersurfaces A., Differential Geometric Structures, McGraw-Hill, New York, 1981
Reference 38
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:36:57.359306Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 284aaafd-d18c-42c3-a0b9-e1bf79ed1389 · outbound
This paper cites an unresolved cited work.
Codimension-Two Spacelike Submanifolds with Umbilical Lightlike Normal Sections and Their Relationship to Lightlike Hypersurfaces Unresolved cited work
Reference 39
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T05:36:57.347275Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation b07cfb27-1ef7-4abc-adda-7a09e7d15f26 · outbound
This paper cites an unresolved cited work.
Codimension-Two Spacelike Submanifolds with Umbilical Lightlike Normal Sections and Their Relationship to Lightlike Hypersurfaces Unresolved cited work
Reference 40
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T05:36:57.335040Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 9d16d8df-6aa6-49ff-af4e-98170d7ffa71 · outbound
This paper cites M., General Relativity, Univ.
Codimension-Two Spacelike Submanifolds with Umbilical Lightlike Normal Sections and Their Relationship to Lightlike Hypersurfaces M., General Relativity, Univ
Reference 41
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:36:57.322323Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Pith citing papers
No inbound Pith citation observations are available.