无正 Ricci 曲率假设下的球面定理与特征值夹挤
微分几何
2019-08-13 v4
摘要
考虑到 Obata 定理的几乎刚性，我们推广了 Petersen 和 Aubry 关于特征值夹挤的球面定理，而不假设 Ricci 曲率的正性，仅假设对于某些正常数 和 有 且 。
引用
@article{arxiv.1808.05317,
title = {Sphere theorems and eigenvalue pinching without positive Ricci curvature assumption},
author = {Masayuki Aino},
journal= {arXiv preprint arXiv:1808.05317},
year = {2019}
}
备注
77 pages v2: minor change v3: an application to the almost umbilical manifolds was added v3: some simplifications and improvements