Nearly Kaehler geometry and Riemannian foliations

Details Nearly Kaehler geometry and Riemannian foliations Nearly Kaehler geometry and Riemannian foliations

2002-03-05

arxiv.org/abs/math/0203038v1

Mathematics

Differential Geometry

28 pages

Scientific paper

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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