Nearly Kaehler geometry and Riemannian foliations
By P. Nagy. 2002
166 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/3c3d9162ac6cc9f6351a6e0c168f496e43ac6ab9
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In Applied Mathematics
In Astronomy and Astrophysics
In Geometry and Topology
Citations in the corpus
- Six-Dimensional Nearly Kähler Manifolds of Cohomogeneity One (II) (2009, background): “Recently Nagy proved the following two structure results: a) any NK manifold is locally holomorphically isometric to the product of a Kähler manifold and a strict NK manifold; b) any complete strict NK manifold is finitely covered by a product of homogeneous 3-symmetric manifolds, twistor spaces of ”
- Homogeneous nearly K\"{a}hler manifolds (2006, background): “Finally, irreducible nearly Khler manifolds are (i) 3-symmetric of type B or (ii) 6-dimensional. c. Eventually, Nagy has proved in [36], corollary 3.1, that the complete, simply connected, real reducible, nearly Khler manifolds are 3-symmetric of type C.”