洛伦兹流形上Killing向量场的Gauss-Bonnet-Chern型障碍
微分几何
2024-07-29 v2
摘要
给出了一个关于偶数维（奇数维）洛伦兹流形上类时（类光）Killing或共形Killing向量场X存在性的新曲率障碍，用其类时（类光）截面曲率表示。作为紧致情形的推论，著名的Gauss-Bonnet-Chern障碍从非零常截面曲率扩展到X上的非零类时截面曲率。
引用
@article{arxiv.2404.07284,
title = {A Gauss-Bonnet-Chern type obstruction for Killing vector fields on Lorentzian manifolds},
author = {Alfonso Romero and Miguel Sánchez},
journal= {arXiv preprint arXiv:2404.07284},
year = {2024}
}
备注
v2: Remark 6 and one reference included. 12 pages, no figures