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}
}