Nearly Kaehler geometry and Riemannian foliations

Paul-Andi Nagy

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arXiv · math/0203038

Nearly Kaehler geometry and Riemannian foliations

Paul-Andi Nagy

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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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Paul-Andi Nagy. 2002-03-05. Nearly Kaehler geometry and Riemannian foliations. https://arxiv.org/abs/math/0203038

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