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arXiv · 2204.01217

Multiplier Hermitian-Einstein metrics on Fano manifolds of KSM-type

Yasuhiro Nakagawa·Satoshi Nakamura
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Abstract

In this article we focus on multiplier Hermitian-Einstein metrics introduced by Mabuchi which include K\"ahler-Einstein metrics, K\"ahler-Ricci solitons and Mabuchi solitons as special cases. We also focus on KSM-manifolds, which are introduced by the first author as toric bundles, to establish a criterion for the existence of multiplier Hermitian-Einstein metrics in terms of KSM-data. An explicit example for a KSM-manifold admitting a family of multiplier Hermitian-Einstein metrics is constructed by using a continuous path connecting a K\"ahler-Ricci soliton and a Mabuchi soliton.

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Yasuhiro Nakagawa, Satoshi Nakamura. 2022-04-04. Multiplier Hermitian-Einstein metrics on Fano manifolds of KSM-type. https://arxiv.org/abs/2204.01217

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