Does negative type characterize the round sphere?
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- by Simon Lyngby Kokkendorff PDF
- Proc. Amer. Math. Soc. 135 (2007), 3695-3702 Request permission
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 $1$ 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 $1$ must be of negative type and that the only compact Riemannian symmetric spaces of negative type are the round spheres.References
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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
- Received by editor(s): August 24, 2006
- Published electronically: August 7, 2007
- Additional Notes: The author was supported by the Danish Research Agency
- Communicated by: Jon G. Wolfson
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 3695-3702
- MSC (2000): Primary 51K99, 53C35, 31C99
- DOI: https://doi.org/10.1090/S0002-9939-07-08951-4
- MathSciNet review: 2336586