黎曼流形中的 Hopf 型定理
微分几何
2022-03-15 v1 偏微分方程分析
复变函数
摘要
1951 年，H. Hopf 证明了欧几里得空间中唯一同胚于球面且具有常平均曲率的曲面是标准的（几何）球面。本文中我们综述 Renato Tribuzy 在推广 Hopf 结果方面的一些贡献，以及作者近期利用这些技术针对曲率流收缩孤立子以及三维扭曲积流形（特别是 de Sitter-Schwarzschild 与 Reissner-Nordstrom 流形）中曲面所得的一些结果。
引用
@article{arxiv.2203.06270,
title = {Hopf type theorems in Riemannian manifolds},
author = {Hilário Alencar and Gregório Silva Neto and Detang Zhou},
journal= {arXiv preprint arXiv:2203.06270},
year = {2022}
}
备注
26 pages. Survey article about the contributions of Renato Tribuzy and the authors to the study of the Hopf's differential of surfaces immersed in Riemannian manifolds. Accepted to be published in a special volume of the Matem\'atica Contempor\^anea, a journal of the Brazilian Mathematical Society, in honor of Renato de Azevedo Tribuzy on the occasion of his 75th birthday