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.
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