Smooth diameter and eigenvalue rigidity in positive Ricci curvature

Author:
Wilderich Tuschmann

Journal:
Proc. Amer. Math. Soc. **130** (2002), 303-306

MSC (2000):
Primary 53C20

DOI:
https://doi.org/10.1090/S0002-9939-01-06384-5

Published electronically:
July 31, 2001

MathSciNet review:
1855649

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A recent injectivity radius estimate and previous sphere theorems yield the following smooth diameter sphere theorem for manifolds of positive Ricci curvature: For any given and there exists a positive constant such that any -dimensional complete Riemannian manifold with Ricci curvature , sectional curvature and diameter is Lipschitz close and diffeomorphic to the standard unit -sphere. A similar statement holds when the diameter is replaced by the first eigenvalue of the Laplacian.

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Additional Information

**Wilderich Tuschmann**

Affiliation:
Max-Planck-Institute for Mathematics in the Sciences, Inselstrasse, D-04103 Leipzig, Germany

Email:
tusch@mis.mpg.de

DOI:
https://doi.org/10.1090/S0002-9939-01-06384-5

Keywords:
Sphere theorems,
injectivity radius,
exotic spheres,
positive Ricci curvature

Received by editor(s):
October 26, 2000

Published electronically:
July 31, 2001

Communicated by:
Wolfgang Ziller

Article copyright:
© Copyright 2001
American Mathematical Society