Bismut Einstein metrics on compact complex manifolds
Differential Geometry
2023-07-27 v4
Abstract
We observe that, for a Bismut Einstein metric, the (2,0)-part of Bismut Ricci form is an eigenvector of the Chern Laplacian. With the help of this observation, we prove that a Bismut Einstein metric with non-zero Einstein constant is K\"ahler Einstein. Additionally, for Bismut Einstein metrics with zero Einstein constant, we prove that they are actually Bismut Ricci flat.
Keywords
Cite
@article{arxiv.2212.04060,
title = {Bismut Einstein metrics on compact complex manifolds},
author = {Yanan Ye},
journal= {arXiv preprint arXiv:2212.04060},
year = {2023}
}