Positive Ricci Curvature and the Length of a shortest periodic geodesic

2022/03/17 by Rotman, Regina
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2203.09492

Abstract

Let Mⁿ be a closed Riemannian manifold of dimension n≥ 2, with Ricci curvature Ric ≥ n-1. We will show that any sphere of dimension m in the space of closed loops on Mⁿ is homotopic to the sphere in the space of closed loops of length at most 8 πm. It follows that the length of a shortest periodic geodesic on Mⁿ is bounded from above by 8 π(n-1).

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