English

Integral Curvature Bounds and Betti Numbers

Differential Geometry 2022-11-11 v1

Abstract

We introduce an upper bound of the Betti numbers of a compact Riemannian manifold given integral bounds on the average of the lowest eigenvalues of the curvature operator. We then establish a new curvature condition for the Betti numbers to vanish using the Bochner technique. This generalizes results from Gallot and Petersen-Wink.

Keywords

Cite

@article{arxiv.2211.05176,
  title  = {Integral Curvature Bounds and Betti Numbers},
  author = {Runze Yu},
  journal= {arXiv preprint arXiv:2211.05176},
  year   = {2022}
}

Comments

9 pages

R2 v1 2026-06-28T05:33:03.120Z