Hermitian Curvature Flow
Differential Geometry
2009-01-26 v3
Abstract
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.
Cite
@article{arxiv.0804.4109,
title = {Hermitian Curvature Flow},
author = {Jeffrey Streets and Gang Tian},
journal= {arXiv preprint arXiv:0804.4109},
year = {2009}
}
Comments
34 pages