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Bibliographic Details
Main Author:	Yao, Qi
Format:	Preprint
Published:	2020
Subjects:	Differential Geometry
Online Access:	https://arxiv.org/abs/2012.04496
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Table of Contents:

Let $G$ be a simply-connected semisimple compact Lie group, $X$ a compact Kähler manifold homogeneous under $G$, and $L$ a negative $G$-equivariant holomorphic line bundle over $X$. We prove that all $G$-invariant Kähler metrics on the total space of $L$ arise from the Calabi ansatz. Using this, we then show that there exists a unique $G$-invariant scalar-flat Kähler metric in each Kähler class of $L$.