The length of the shortest closed geodesics on a positively curved manifold

TL;DR

This paper characterizes the Euclidean sphere among positively curved manifolds by relating sectional curvature bounds to the minimal length of closed geodesics.

Contribution

It provides a metric-based characterization of the Euclidean sphere using curvature bounds and geodesic length criteria.

Findings

Euclidean sphere uniquely characterized by geodesic length and curvature

Lower bounds on sectional curvature imply specific geodesic length properties

New metric criteria for identifying the Euclidean sphere in positive curvature settings

Abstract

We give a metric characterization of the Euclidean sphere in terms of the lower bound of the sectional curvature and the length of the shortest closed geodesics.