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Boundary and lens rigidity of finite quotients


Author: Christopher Croke
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
Published electronically: June 8, 2005
MathSciNet review: 2163605
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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.


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Additional Information

Christopher Croke
Affiliation: Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6395
Email: ccroke@math.upenn.edu

DOI: https://doi.org/10.1090/S0002-9939-05-07927-X
Keywords: Boundary rigidity, lens rigidity, quotients
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
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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