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Nearly Kaehler geometry and Riemannian foliations

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Paul-Andi Nagy

Differential Geometry · Submitted 5 Mar 2002

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We show that a strict and complete nearly Kaehler is locally a Riemannian product of homogenous nearly Kaehler spaces, twistor spaces over quaternionic Kaehler manifolds and 6-dimensional nearly Kaehler manifolds.

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arXiv IDmath/0203038 (version 1)
Pith IDF4ENDMPB, Pith's permanent record of this paper and its review
CitationPaul-Andi Nagy. "Nearly Kaehler geometry and Riemannian foliations." arXiv:math/0203038 (2002). https://pith.science/paper/F4ENDMPB
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,218 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.12 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.32 · compares with prior results 0.28 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We consider strict and complete nearly Kaehler manifolds with the canonical Hermitian connection. The holonomy representation of the canonical Hermitian connection is studied. We show that a strict and complete nearly Kaehler is locally a Riemannian product of homogenous nearly Kaehler spaces, twistor spaces over quaternionic Kaehler manifolds and 6-dimensional nearly Kaehler manifolds. As an application we obtain structure results for totally geodesic Riemannian foliations admitting a compatible Kaehler structure. Finally, we obtain a classification result for the homogenous case, reducing a conjecture of Wolf and Gray to its 6-dimensional form.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We consider strict and complete nearly Kaehler manifolds with the canonical Hermitian connection. background 0.66 0.48 0.03 unclear 0.63
s1 The holonomy representation of the canonical Hermitian connection is studied. contribution 0.88 0.77 0.03 asserted 0.66
s2 We show that a strict and complete nearly Kaehler is locally a Riemannian product of homogenous nearly Kaehler spaces, twistor spaces over quaternionic Kaehler manifolds and 6-dimensional nearly Kaehler manifolds. result 1.00 0.95 0.82 asserted 1.00
s3 As an application we obtain structure results for totally geodesic Riemannian foliations admitting a compatible Kaehler structure. result 0.87 0.93 0.09 asserted 1.00
s4 Finally, we obtain a classification result for the homogenous case, reducing a conjecture of Wolf and Gray to its 6-dimensional form. result 0.95 0.94 0.23 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

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not examined
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  • figures and tables
  • references and citing sentences
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  • P abstract
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  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We consider strict and complete nearly Kaehler manifolds with the canonical Hermitian connection. The holonomy representation of the canonical Hermitian connection is studied. We show that a strict and complete nearly Kaehler is locally a Riemannian product of homogenous nearly Kaehler spaces, twistor spaces over quaternionic Kaehler manifolds and 6-dimensional nearly Kaehler manifolds. As an application we obtain structure results for totally geodesic Riemannian foliations admitting a compatible Kaehler structure. Finally, we obtain a classification result for the homogenous case, reducing a conjecture of Wolf and Gray to its 6-dimensional form.

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2 arXiv papers cite this in 2 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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Cites it as background 1 paper
  • Gray [ref] , and recently were investigated and classified by Nagy et al [ref] who have shown that the complete and strict nearly Kähler manifolds, i.e. non-Kähler manifolds, are locally Riemannian products of 6-dimensional nearly Kähler manifolds, twistor spaces over quaternionic Kähler manifolds and homogeneous nearly Kähler spaces.

    Gravity and induced matter on Nearly Kahler Manifolds · Introduction · 0.99

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