English

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.

Keywords

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