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June 2015 Maximal Diameter Sphere Theorem for Manifolds with Nonconstant Radial Curvature
Nathaphon BOONNAM
Tokyo J. Math. 38(1): 145-151 (June 2015). DOI: 10.3836/tjm/1437506241

Abstract

We generalize Toponogov's maximal diameter sphere theorem from the radial curvature geometry's standpoint. 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. Furthermore if the diameter of such an $M$ equals that of the ellipsoid, then $M$ is isometric to the $n$-dimensional ellipsoid of revolution.

Citation

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Nathaphon BOONNAM. "Maximal Diameter Sphere Theorem for Manifolds with Nonconstant Radial Curvature." Tokyo J. Math. 38 (1) 145 - 151, June 2015. https://doi.org/10.3836/tjm/1437506241

Information

Published: June 2015
First available in Project Euclid: 21 July 2015

zbMATH: 1327.53048
MathSciNet: MR3374618
Digital Object Identifier: 10.3836/tjm/1437506241

Subjects:
Primary: 53C22

Rights: Copyright © 2015 Publication Committee for the Tokyo Journal of Mathematics

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Vol.38 • No. 1 • June 2015
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