Submanifolds with nonpositive extrinsic curvature
Differential Geometry
2015-07-10 v1
Abstract
We prove that complete submanifolds, on which the Omori-Yau weak maximum principle for the Hessian holds, with low codimension and bounded by cylinders of small radius must have points rich in large positive extrinsic curvature. The lower the codimension is, the richer such points are. The smaller the radius is, the larger such curvatures are. This work unifies and generalizes several previous results on submanifolds with nonpositive extrinsic curvature.
Keywords
Cite
@article{arxiv.1507.02523,
title = {Submanifolds with nonpositive extrinsic curvature},
author = {Samuel Canevari and Guilherme Machado de Freitas and Fernando Manfio},
journal= {arXiv preprint arXiv:1507.02523},
year = {2015}
}
Comments
20 pages. arXiv admin note: text overlap with arXiv:0907.5025 by other authors