Boundary and lens rigidity of finite quotients
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- Proc. Amer. Math. Soc. 133 (2005), 3663-3668 Request permission
Abstract:
We consider compact Riemannian manifolds $(M,\partial M,g)$ with boundary $\partial M$ and metric $g$ on which a finite group $\Gamma$ acts freely. We determine the extent to which certain rigidity properties of $(M,\partial M,g)$ descend to the quotient $(M/\Gamma ,\partial /\Gamma ,g)$. In particular, we show by example that if $(M,\partial M,g)$ is boundary rigid, then $(M/\Gamma ,\partial /\Gamma ,g)$ need not be. On the other hand, lens rigidity of $(M,\partial M,g)$ does pass to the quotient.References
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Additional Information
- Christopher Croke
- Affiliation: Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6395
- MR Author ID: 204906
- Email: ccroke@math.upenn.edu
- Received by editor(s): March 29, 2004
- Received by editor(s) in revised form: August 10, 2004
- Published electronically: June 8, 2005
- Additional Notes: This work was supported by MSRI and NSF grant DMS 02-02536
- Communicated by: Jon G. Wolfson
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 133 (2005), 3663-3668
- MSC (2000): Primary 53C22, 53C24
- DOI: https://doi.org/10.1090/S0002-9939-05-07927-X
- MathSciNet review: 2163605