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Small volume on big  -spheres
Author(s):
Christopher
B.
Croke
Journal:
Proc. Amer. Math. Soc.
136
(2008),
715-717.
MSC (2000):
Primary 53C20
Posted:
November 6, 2007
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Abstract:
We consider Riemannian metrics on the  -sphere for  such that the distance between any pair of antipodal points is bounded below by 1. We show that the volume can be arbitrarily small. This is in contrast to the  -dimensional case where Berger has shown that  .
References:
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Additional Information:
Christopher
B.
Croke
Affiliation:
Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6395
Email:
ccroke@math.upenn.edu
DOI:
10.1090/S0002-9939-07-09079-X
PII:
S 0002-9939(07)09079-X
Received by editor(s):
November 9, 2006
Posted:
November 6, 2007
Additional Notes:
The author was supported by NSF grants DMS 02-02536 and 07-04145
Communicated by:
Jon G. Wolfson
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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