Warped product Kaehler manifolds and Bochner-Kaehler metrics

Details Warped product Kaehler manifolds and Bochner-Kaehler metrics Warped product Kaehler manifolds and Bochner-Kaehler metrics

2006-05-03

arxiv.org/abs/math/0605082v1

Journal of Geometry and Physics, 58 (2008), 7, 803-824.

Mathematics

Differential Geometry

28

Scientific paper

10.1016/j.geomphys.2008.02.002

Using as an underlying manifold an alpha-Sasakian manifold we introduce warped product Kaehler manifolds. We prove that if the underlying manifold is an alpha-Sasakian space form, then the corresponding Kaehler manifold is of quasi-constant holomorphic sectional curvatures with special distribution. Conversely, we prove that any Kaehler manifold of quasi-constant holomorphic sectional curvatures with special distribution locally has the structure of a warped product Kaehler manifold whose base is an alpha-Sasakian space form. Considering the scalar distribution generated by the scalar curvature of a Kaehler manifold, we give a new approach to the local theory of Bochner-Kaehler manifolds. We study the class of Bochner-Kaehler manifolds whose scalar distribution is of special type. Taking into account that any manifold of this class locally is a warped product Kaehler manifold, we describe all warped product Bochner-Kaehler metrics. We find four families of complete metrics of this type.

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