The canonical contact structure on the space of oriented null geodesics of pseudospheres and products
-
Yamile Godoy
and
Marcos Salvai
Abstract
Let Sk,m be the pseudosphere of signature (k,m). We show that the space ℒ0(Sk,m) of all oriented null geodesics in Sk,m is a manifold, and we describe geometrically its canonical contact distribution in terms of the space of oriented geodesics of certain totally geodesic degenerate hypersurfaces in Sk;m. Further, we find a contactomorphism with some standard contact manifold, namely, the unit tangent bundle of some pseudo-Riemannian manifold. Also, we express the null billiard operator on ℒ0(Sk,m) associated with some simple regions in Sk;m in terms of the geodesic flows of spheres. For the pseudo-Riemannian product N of two complete Riemannian manifolds, we give geometrical conditions on the factors for ℒ0(N) to be manifolds and exhibit a contactomorphism with some standard contact manifold.
© 2013 by Walter de Gruyter GmbH & Co.
Articles in the same Issue
- Masthead
- Some remarks on Nijenhuis brackets, formality, and Kähler manifolds
- Semifields from skew polynomial rings
- A note on CR quaternionic maps
- On maximal curves of Fermat type
- On the singular locus of sets definable in a quasianalytic structure
- A product integral representation of mixed volumes of two convex bodies
- The Tutte polynomial of the Sierpiński and Hanoi graphs
- A lower bound for the Ricci curvature of submanifolds in generalized Sasakian space forms
- The canonical contact structure on the space of oriented null geodesics of pseudospheres and products
- Inscribable stacked polytopes
- Differential Harnack estimates for backward heat equations with potentials under an extended Ricci flow
Articles in the same Issue
- Masthead
- Some remarks on Nijenhuis brackets, formality, and Kähler manifolds
- Semifields from skew polynomial rings
- A note on CR quaternionic maps
- On maximal curves of Fermat type
- On the singular locus of sets definable in a quasianalytic structure
- A product integral representation of mixed volumes of two convex bodies
- The Tutte polynomial of the Sierpiński and Hanoi graphs
- A lower bound for the Ricci curvature of submanifolds in generalized Sasakian space forms
- The canonical contact structure on the space of oriented null geodesics of pseudospheres and products
- Inscribable stacked polytopes
- Differential Harnack estimates for backward heat equations with potentials under an extended Ricci flow
