Maximal diameter sphere theorem for manifolds with nonconstant radial curvature

2013/11/19 by Nathaphon Boonnam, Boonnam, Nathaphon
Mathematics · #53C22 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53C22

paper · pdf · doi:10.48550/arxiv.1311.4631

7 pages, no figures

arxiv created 2013/11/19 · arxiv updated 2013/11/20

Abstract

We generalize the maximal diameter sphere theorem due to Toponogov by means of the radial curvature. As a corollary to our main theorem, we prove that for a complete connected Riemannian n-manifold M having radial sectional curvature at a point bounded from below by the radial curvature function of an ellipsoid of prolate type, the diameter of M does not exceed the diameter of the ellipsoid, and if the diameter of M equals that of the ellipsoid, then M is isometric to the n-dimensional ellipsoid of revolution.

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