Integral Curvature Bounds and Betti Numbers

2022/11/09 by Yu, Runze · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2211.05176

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.

Cited by

• Curvature operator and Euler number

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