带密度黎曼流形的截面曲率
微分几何
2015-01-27 v3
摘要
本文引入了带密度黎曼流形的两种新的截面曲率概念。在这两种曲率概念下，我们对常曲率流形进行了分类。我们还证明了 Cartan-Hadamard 定理、Synge 定理和 Bonnet-Myers 定理的推广形式，以及（非光滑）1/4 夹球定理的推广形式。主要思想是修正径向曲率方程和第二变分公式，然后将经典黎曼几何的技术应用于这些新方程。
引用
@article{arxiv.1311.0267,
title = {Sectional curvature for Riemannian manifolds with density},
author = {William Wylie},
journal= {arXiv preprint arXiv:1311.0267},
year = {2015}
}
备注
19 pages, The expositiion of the paper has been shortened by a few pages and some of the arguments streamlined at the suggestion of the referee. Final version, to appear in Geometriae Dedicata