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- W2993114682 abstract "Let S be a compact oriented surface of constant curvature −1 and let T 1S be the unit tangent bundle of S endowed with the canonical (Sasaki) metric. We prove that T 1S has dense periodic geodesics, that is, the set of vectors tangent to periodic geodesics in T 1S is dense in TT 1S. Let M be a compact Riemannian manifold. M is said to have the DPG property (density of periodic geodesics) if the vectors tangent to periodic geodesics in M are dense in TM, the tangent bundle of M. A compact manifold is known to have this property if, for example, its geodesic flow is Anosov (see [1]), in particular if it is hyperbolic. In this note we prove that the unit tangent bundle of a compact oriented surface of constant curvature −1 shares with the surface the DPG property. ∗Partially supported by conicor, ciem (conicet) and secyt (unc). Mathematical Subject Classification: 53C 22, 53 C 30, 58F 17" @default.
- W2993114682 created "2019-12-13" @default.
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- W2993114682 date "1999-01-01" @default.
- W2993114682 modified "2023-09-26" @default.
- W2993114682 title "Density of periodic geodesics in the unit tangent bundle of a compact hyperbolic surface" @default.
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