Spherical points in Riemannian manifolds

Author:
Benjamin Schmidt

Journal:
Proc. Amer. Math. Soc. **139** (2011), 305-308

MSC (2010):
Primary 53B21; Secondary 53C20, 53C22, 53C24, 53C45

Published electronically:
August 5, 2010

MathSciNet review:
2729092

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Abstract | References | Similar Articles | Additional Information

Abstract: A point in a Riemannian manifold is weakly spherical if for each point there is either exactly one or at least three minimizing geodesic segments joining to . In this note, it is shown that round 2-dimensional spheres are the only Riemannian surfaces with a weakly spherical point realizing the injectivity radius.

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Additional Information

**Benjamin Schmidt**

Affiliation:
Department of Mathematics, Michigan State University, East Lansing, Michigan 48824

Email:
schmidt@math.msu.edu

DOI:
https://doi.org/10.1090/S0002-9939-2010-10521-X

Received by editor(s):
December 10, 2009

Received by editor(s) in revised form:
March 30, 2010

Published electronically:
August 5, 2010

Additional Notes:
The author was supported in part by NSF Grant DMS-0905906.

Communicated by:
Jon G. Wolfson

Article copyright:
© Copyright 2010
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.