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arXiv · 1801.08303

Stability of nonnegative isotropic curvature under continuous deformations of the metric

Thomas Richard
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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.

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Thomas Richard. 2018-01-25. Stability of nonnegative isotropic curvature under continuous deformations of the metric. https://arxiv.org/abs/1801.08303

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