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Homology Vanishing Theorems for Pinched Submanifolds

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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. Homology vanishing results are given that strengthen and sharpen previous ones. In addition, an integral bound is provided for the Bochner operator of compact Euclidean submanifolds in terms of the Betti numbers.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Cyprus, 1678, Nicosia, Cyprus

    Christos-Raent Onti

  2. Department of Mathematics, University of Ioannina, 45110, Ioannina, Greece

    Theodoros Vlachos

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  1. Christos-Raent Onti
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  2. Theodoros Vlachos
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Onti, CR., Vlachos, T. Homology Vanishing Theorems for Pinched Submanifolds. J Geom Anal 32, 294 (2022). https://doi.org/10.1007/s12220-022-01032-9

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