Hermitian Curvature Flow

Details Hermitian Curvature Flow Hermitian Curvature Flow

2008-04-25

arxiv.org/abs/0804.4109v3

Mathematics

Differential Geometry

34 pages

Scientific paper

We define a functional for Hermitian metrics using the curvature of the Chern connection. The Euler-Lagrange equation for this functional is an elliptic equation for Hermitian metrics. Solutions to this equation are related to K\"ahler-Einstein metrics, and are automatically K\"ahler-Einstein under certain conditions. Given this, a natural parabolic flow equation arises. We prove short time existence and regularity results for this flow, as well as stability for the flow near K\"ahler-Einstein metrics with negative or zero first Chern class.

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