Rigidity of surfaces whose geodesic flows preserve smooth foliations of codimension 1
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- by José Barbosa Gomes and Rafael O. Ruggiero PDF
- Proc. Amer. Math. Soc. 135 (2007), 507-515 Request permission
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.References
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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
- MR Author ID: 313673
- Email: rorr@mat.puc-rio.br
- 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
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 507-515
- MSC (2000): Primary 53C24; Secondary 53C22, 57R30, 37D40
- DOI: https://doi.org/10.1090/S0002-9939-06-08755-7
- MathSciNet review: 2255297