Rigidity of Riemannian manifolds containing an equator

Abstract: If a Riemannian sphere S^2 with curvature between 0 and 1 has a closed geodesic of length 2\pi, then its curvature is constant and equal to 1. This result is due to Calabi. In dimension 3 and under the same curvature assumptions, the existence of a minimal sphere of area 4\pi rigidifies the metric. This result has been obtained in a preceding work with H. Rosenberg. In this talk, I will explain how this work can be generalized in higher dimension. As a consequence, I will also give a rigidity result concerning Simon-Smith width.

differential geometry

Audience: researchers in the topic

Geometric Analysis in the Large