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Geodesic Flows on Manifolds of Negative Curvature with Smooth Horospheric Foliations


Feres, Renato (1989) Geodesic Flows on Manifolds of Negative Curvature with Smooth Horospheric Foliations. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/f6yt-bf73.


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 C Riemannian manifold of negative sectional curvature. Assume the stable or unstable foliation of the geodesic flow φt: V → V on the unit tangent bundle V of M is C. Assume moreover that either (a) the sectional curvature of M satisfies -4 < K ≤ -1 or (b) the dimension of M is odd. Then the geodesic flow of M is C-isomorphic (i. e., conjugate under a C 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.))
Subject Keywords:Mathematics
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Kechris, Alexander S.
Thesis Committee:
  • Katok, Anatole (chair)
  • Luxemburg, W. A. J.
  • Ramakrishnan, Dinakar
  • Kechris, Alexander S.
Defense Date:10 May 1989
Funding AgencyGrant Number
Alfred P. Sloan FoundationUNSPECIFIED
Record Number:CaltechETD:etd-05232007-115904
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1988
Deposited By: Imported from ETD-db
Deposited On:24 May 2007
Last Modified:14 Jul 2021 21:47

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