Pith Number

pith:JZGITLPJ

pith:2026:JZGITLPJBPX5NMJZQ5D7K6QEYF

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\lambda-biharmonic Riemannian submersions from manifolds with constant sectional curvature

Miho Shito, Shun Maeta

λ-biharmonic Riemannian submersions from constant curvature manifolds do not exist except when curvature is negative and λ takes the critical value.

arxiv:2605.15578 v1 · 2026-05-15 · math.DG

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

We prove non-existence results for λ-biharmonic Riemannian submersions from (n + 1)-dimensional Riemannian manifolds with constant sectional curvature c to n-dimensional Riemannian manifolds. Our results show that the critical value λ = 2(n - 1)c plays a decisive role.

C2weakest assumption

The domain manifold is assumed to have constant sectional curvature c, which is invoked to simplify the bitension field equation and obtain the non-existence statements under the stated conditions on λ.

C3one line summary

Non-existence results for λ-biharmonic Riemannian submersions from constant-curvature (n+1)-manifolds to n-manifolds, plus constructions when λ equals the critical value in negative curvature.

References

38 extracted · 38 resolved · 1 Pith anchors

[1] M. A. Akyol and Y.-L. Ou,Biharmonic Riemannian submersions, Ann. Mat. Pura Appl. (4)198(2019), no. 2, 559–570 2019

[2] A. Balmu¸ s, S. Montaldo and C. Oniciuc,Classification results for biharmonic submanifolds in spheres, Israel J. Math.168(2008), 201–220 2008

[3] A. Balmu¸ s, S. Montaldo and C. Oniciuc,Biharmonic hypersurfaces in 4-dimensional space forms, Math. Nachr.283(2010), no. 12, 1696–1705 2010

[4] H. Bibi, E. Loubeau and C. Oniciuc,Unique continuation property for biharmonic hypersurfaces in spheres, Ann. Global Anal. Geom.60(2021), no. 4, 807–827 2021

[5] R. Caddeo, S. Montaldo and C. Oniciuc,Biharmonic submanifolds ofS 3, Internat J. Math.12(2001), no. 8, 867–876 2001

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-20T00:01:06.386665Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4e4c89ade90befd6b1398747f57a04c154528d6d1317f51e7b7d76cc4e7a20cd

Aliases

arxiv: 2605.15578 · arxiv_version: 2605.15578v1 · doi: 10.48550/arxiv.2605.15578 · pith_short_12: JZGITLPJBPX5 · pith_short_16: JZGITLPJBPX5NMJZ · pith_short_8: JZGITLPJ

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/JZGITLPJBPX5NMJZQ5D7K6QEYF \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 4e4c89ade90befd6b1398747f57a04c154528d6d1317f51e7b7d76cc4e7a20cd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a5a00470772b82e4818e63efd163b88bbca19b5e801154ef804ded89be30e898",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2026-05-15T03:40:36Z",
    "title_canon_sha256": "e32f424c5af186be53ea8af2a9ed722758dd9d27d847eaeda34b75d429b6e955"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15578",
    "kind": "arxiv",
    "version": 1
  }
}