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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Rigidity of surfaces whose geodesic flows preserve smooth foliations of codimension 1


Authors: José Barbosa Gomes and Rafael O. Ruggiero
Journal: Proc. Amer. Math. Soc. 135 (2007), 507-515
MSC (2000): Primary 53C24; Secondary 53C22, 57R30, 37D40
Published electronically: August 28, 2006
MathSciNet review: 2255297
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Abstract: Let $ S$ be a closed orientable surface. Assume that there exists a codimension one foliation $ \mathcal F$ of class $ C^3$ in the unit tangent bundle of $ S$, whose leaves are invariant under the geodesic flow of $ S$. Then, the curvature of $ S$ is a nonpositive constant.


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Additional Information

José Barbosa Gomes
Affiliation: Departamento de Matemática, Universidade Federal de Juiz de Fora, Juiz de Fora, MG, Brazil, 36036-330
Email: jbarbosa@ice.ufjf.br

Rafael O. Ruggiero
Affiliation: Departamento de Matemática, Pontifícia Universidade Católica do Rio de Janeiro, Rio de Janeiro, RJ, Brazil, 22453-900
Email: rorr@mat.puc-rio.br

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08755-7
PII: S 0002-9939(06)08755-7
Keywords: Godbillon-Vey number, geodesic flow, rigidity, Anosov flow
Received by editor(s): September 14, 2005
Published electronically: August 28, 2006
Additional Notes: The first author was supported in part by CAPES of the Brazilian Government.
The second author was supported in part by CNPq of the Brazilian Government
Communicated by: Michael Handel
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.