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

Gomes, José; Ruggiero, Rafael

doi:10.1090/S0002-9939-06-08755-7

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.

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