Homology vanishing theorems for pinched submanifolds
Christos-Raent Onti, Theodoros Vlachos
TL;DR
This paper explores the topology of submanifolds satisfying specific curvature pinching conditions, establishing homology vanishing theorems and providing bounds on the Bochner operator related to Betti numbers.
Contribution
It introduces new homology vanishing theorems for submanifolds under extrinsic curvature pinching conditions and offers integral bounds for the Bochner operator.
Findings
Homology vanishing results for submanifolds under pinching conditions
Integral bounds for the Bochner operator in terms of Betti numbers
Connections between extrinsic invariants and topological properties
Abstract
We investigate the geometry and topology of submanifolds under a sharp pinching condition involving extrinsic invariants like the mean curvature and the length of the second fundamental form. Several homology vanishing results are given. Moreover, an integral bound is provided for the Bochner operator of compact Euclidean submanifolds in terms of the Betti numbers.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometric and Algebraic Topology · Topological and Geometric Data Analysis