English

Homology vanishing theorems for pinched submanifolds

Differential Geometry 2022-07-21 v3

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.

Keywords

Cite

@article{arxiv.2105.12716,
  title  = {Homology vanishing theorems for pinched submanifolds},
  author = {Christos-Raent Onti and Theodoros Vlachos},
  journal= {arXiv preprint arXiv:2105.12716},
  year   = {2022}
}