Integral Curvature Bounds and Betti Numbers

Runze Yu

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arXiv · 2211.05176

Integral Curvature Bounds and Betti Numbers

Runze Yu

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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.

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BibTeX RIS

Runze Yu. 2022-11-09. Integral Curvature Bounds and Betti Numbers. https://arxiv.org/abs/2211.05176

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