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Geodesic flows on manifolds of negative curvature with smooth horospheric foliations

Citation

Feres, Renato (1989) Geodesic flows on manifolds of negative curvature with smooth horospheric foliations. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-05232007-115904

Abstract

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We improve a result due to M. Kanai on the rigidity of geodesic flows on closed Riemannian manifolds of negative curvature whose stable or unstable (horospheric) foliation is smooth. More precisely, the main result proven here is: Let M be a closed [...] Riemannian manifold of negative sectional curvature. Assume the stable or unstable foliation of the geodesic flow [...] on the unit tangent bundle V of M is [...]. Assume moreover that either (a) the sectional curvature of M satisfies [...] or (b) the dimension of M is odd. Then the geodesic flow of M is [...]-isomorphic (i. e., conjugate under a [...] diffeomorphism between the unit tangent bundles) to the geodesic flow on a closed Riemannian manifold of constant negative curvature.

Item Type:Thesis (Dissertation (Ph.D.))
Degree Grantor:California Institute of Technology
Major Option:Mathematics
Thesis Availability:Restricted to Caltech community only
Thesis Committee:
  • Katok, Anatole (chair)
Defense Date:10 May 1989
Record Number:CaltechETD:etd-05232007-115904
Persistent URL:http://resolver.caltech.edu/CaltechETD:etd-05232007-115904
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1988
Collection:CaltechTHESIS
Deposited By: Imported from ETD-db
Deposited On:24 May 2007
Last Modified:26 Dec 2012 02:45

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