Brown-York mass and positive scalar curvature II: Besse's conjecture and related problems
Brown-York mass and positive scalar curvature II: Besse's conjecture and related problems
复制标题
布朗约克质量和正标量曲率 II：贝塞猜想及相关问题
DOI：
10.1007/s10455-019-09653-0
复制
发表时间：
2019
影响因子：
0.7
通讯作者：
Yuan Wei
中科院分区：
文献类型：
--
作者：
Fang Yi;Yuan Wei
贝塞猜想是亚瑟L. Besse，它描述了具有单位体积和常数量曲率约束的希尔伯特-爱因斯坦泛函的临界点。在这篇文章中，我们表明有一个有趣的联系之间的贝塞猜想和布朗约克质量的正质量定理。借助于正质量定理，我们研究了CPE流形的几何结构，从而对Besse猜想有了进一步的理解。作为相关的主题，我们也讨论了V-静态度量的相应结果。
The Besse’s conjecture was posed on the well-known bookEinstein manifoldsby Arthur L. Besse, which describes critical points of Hilbert–Einstein functional with constraint of unit volume and constant scalar curvature. In this article, we show that there is an interesting connection between Besse’s conjecture and positive mass theorem for Brown–York mass. With the aid of positive mass theorem, we investigate the geometric structure of CPE manifolds and this provides us further understandings about Besse’s conjecture. As a related topic, we also discuss corresponding results forV-static metrics.