Integral of scalar curvature on manifolds with a pole
Differential Geometry
2024-08-21 v1
Abstract
On any complete three dimensional Riemannian manifold with a pole and non-negative Ricci curvature, we show that the asymptotic scaling invariant integral of scalar curvature, is equal to a term determined by the asymptotic volume ratio of this Riemannian manifold.
Cite
@article{arxiv.2306.07460,
title = {Integral of scalar curvature on manifolds with a pole},
author = {Guoyi Xu},
journal= {arXiv preprint arXiv:2306.07460},
year = {2024}
}
Comments
A formula is proved, to appear in Proceedings of the American Mathematical Society