Spherical points in Riemannian manifolds
Author:
Benjamin Schmidt
Journal:
Proc. Amer. Math. Soc. 139 (2011), 305308
MSC (2010):
Primary 53B21; Secondary 53C20, 53C22, 53C24, 53C45
Published electronically:
August 5, 2010
MathSciNet review:
2729092
Fulltext PDF
Abstract 
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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 2dimensional spheres are the only Riemannian surfaces with a weakly spherical point realizing the injectivity radius.
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 J. Hebda, Metric structure of cut loci in surfaces and Ambrose's problem, J. Diff. Geom. 40 (1994), 621642. . MR 1305983 (95m:53046)
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 T. Zamfirescu, On some questions about convex surfaces, Math. Nachr. 172 (1995), 313324. MR 1330637 (96e:52004)
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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:
http://dx.doi.org/10.1090/S00029939201010521X
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 DMS0905906.
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.
