Geometry of Hermitian manifolds

Details Geometry of Hermitian manifolds Geometry of Hermitian manifolds

2010-10-31

arxiv.org/abs/1011.0207v2

Mathematics

Differential Geometry

Scientific paper

On Hermitian manifolds, the second Ricci curvature tensors of various metric connections are closely related to the geometry of Hermitian manifolds. By refining the Bochner formulas for any Hermitian complex vector bundle (Riemannain real vector bundle) with an arbitrary metric connection over a compact Hermitian manifold, we can derive various vanishing theorems for Hermitian manifolds and complex vector bundles by the second Ricci curvature tensors. We will also introduce a natural geometric flow on Hermitian manifolds by using the second Ricci curvature tensor.

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