带边紧流形上曲率的存在性与障碍
微分几何
2024-09-04 v2
摘要
研究给定带边紧流形所能具有的曲率函数集合。首先，证明高斯-博内定理所要求的符号是给定函数成为某个共形等价度量的测地曲率或高斯曲率的充要条件。我们的方法使我们能够解决在逐点共形情形下无法解决的问题。此外，我们获得了关于逐点共形变形的更深入、更精细的信息。在共形设定下，我们证明了具有指定曲率的度量的新的存在性与不存在性结果，这些结果依赖于欧拉示性数。
引用
@article{arxiv.2204.03582,
title = {Existence and obstructions for the curvature on compact manifolds with boundary},
author = {Tiarlos Cruz and Almir Silva Santos and Feliciano Vitório},
journal= {arXiv preprint arXiv:2204.03582},
year = {2024}
}
备注
Title changed. We split the first version of this paper in two. This one corresponds to the results concerned with compact manifolds (Theorems 1.1, 1.2 and 1.3). The results for the non-compact manifold will appear in a more complete paper. Accepted for publication in Communications in Contemporary Mathematics