Bismut Einstein metrics on compact complex manifolds

Yanan Ye

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arXiv · 2212.04060

Bismut Einstein metrics on compact complex manifolds

Yanan Ye

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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.

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Yanan Ye. 2022-12-08. Bismut Einstein metrics on compact complex manifolds. https://arxiv.org/abs/2212.04060

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