关于预设 Ricci 曲率泛函的变分性质
微分几何
2023-09-18 v2
摘要
我们研究齐性度量的预设 Ricci 曲率问题。给定 (0,2)-张量场 ，该问题求解方程 （其中 为某常数）的解。我们的方法基于考察标量曲率泛函的全局性质，其临界点即为该方程的解。我们给出了一般齐性空间存在全局最大值的条件。最后，我们在具体例子中研究该泛函的行为以阐明我们的结果。
关键词
引用
@article{arxiv.2110.14129,
title = {On the variational properties of the prescribed Ricci curvature functional},
author = {Artem Pulemotov and Wolfgang Ziller},
journal= {arXiv preprint arXiv:2110.14129},
year = {2023}
}
备注
24 pages, 3 figures. Version 2: A portion of this paper has been generalised and moved to the new paper "Palais-Smale sequences for the prescribed Ricci curvature functional"; the current version deals with the question of when the prescribed Ricci curvature functional assumes its maximum