English

Stability of nonnegative isotropic curvature under continuous deformations of the metric

Differential Geometry 2018-01-26 v1

Abstract

Using a method introduced by R. Bamler to study the behavior of scalar curvature under continuous deformations of Riemannian metrics, we prove that if a sequence of smooth Riemannian metrics gi on a fixed compact manifold M has isotropic curvature bounded from below by a nonnegative function u, and if gi converge in C 0 norm to a smooth metric g, then g has isotropic curvature bounded from below by u. The proof also works for various other bounds from below on the curvature, such has non-negative curvature operator.

Keywords

Cite

@article{arxiv.1801.08303,
  title  = {Stability of nonnegative isotropic curvature under continuous deformations of the metric},
  author = {Thomas Richard},
  journal= {arXiv preprint arXiv:1801.08303},
  year   = {2018}
}