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arXiv · 2105.12716

Homology vanishing theorems for pinched submanifolds

Christos-Raent Onti·Theodoros Vlachos
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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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Christos-Raent Onti, Theodoros Vlachos. 2021-05-26. Homology vanishing theorems for pinched submanifolds. https://arxiv.org/abs/2105.12716

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