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Does negative type characterize the round sphere?
Author(s):
Simon
Lyngby
Kokkendorff
Journal:
Proc. Amer. Math. Soc.
135
(2007),
3695-3702.
MSC (2000):
Primary 51K99, 53C35, 31C99
Posted:
August 7, 2007
MathSciNet review:
2336586
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Abstract:
We discuss the measure-theoretic metric invariants extent, mean distance and symmetry ratio and their relation to the concept of negative type of a metric space. A conjecture stating that a compact Riemannian manifold with symmetry ratio  must be a round sphere was put forward by the author in 2004. We resolve this conjecture in the class of Riemannian symmetric spaces by showing that a Riemannian manifold with symmetry ratio  must be of negative type and that the only compact Riemannian symmetric spaces of negative type are the round spheres.
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Additional Information:
Simon
Lyngby
Kokkendorff
Affiliation:
Department of Mathematics, Technical University of Denmark, Building 303, 2800 Kgs. Lyngby, Denmark
Email:
S.L.Kokkendorff@mat.dtu.dk
DOI:
10.1090/S0002-9939-07-08951-4
PII:
S 0002-9939(07)08951-4
Received by editor(s):
August 24, 2006
Posted:
August 7, 2007
Additional Notes:
The author was supported by the Danish Research Agency
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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