爱因斯坦型结构、Besse猜想以及共形类中$\varphi$-CPE度量的唯一性结果
微分几何
2024-01-17 v2 偏微分方程分析
摘要
本文研究CPE猜想向流形的推广，其中支持一种将曲率与光滑映射的几何相联系的结构。所得系统记为，从变分观点看是自然的，并描述了限制在单位体积且-数量曲率恒定的度量上、积分-数量曲率泛函的驻点。我们证明了共形类中解的刚性结论，以及刻画支持以为调和映射的的流形中圆球面的间隙定理。
引用
@article{arxiv.2201.00263,
title = {Einstein-type structures, Besse's conjecture and a uniqueness result for a $\varphi$-CPE metric in its conformal class},
author = {Giulio Colombo and Luciano Mari and Marco Rigoli},
journal= {arXiv preprint arXiv:2201.00263},
year = {2024}
}
备注
26 pages. Package axessibility included to make the paper available to visually impaired people. Revised version: the rigidity theorem was improved in the light of a result by Barbosa, Mirandola and Vitorio. We included comments and corrected a mistake in the variational formulation