Artículo
The canonical contact structure on the space of oriented null geodesics of pseudospheres and products
Fecha de publicación:
10/2013
Editorial:
de Gruyter
Revista:
Advances In Geometry
ISSN:
1615-715X
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
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.
Palabras clave:
Contact Manifold
,
Null Geodesic
,
Space of Geodesics
,
Billiards
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Articulos(CIEM)
Articulos de CENT.INV.Y ESTUDIOS DE MATEMATICA DE CORDOBA(P)
Articulos de CENT.INV.Y ESTUDIOS DE MATEMATICA DE CORDOBA(P)
Citación
Godoy, Yamile Alejandra; Salvai, Marcos Luis; The canonical contact structure on the space of oriented null geodesics of pseudospheres and products; de Gruyter; Advances In Geometry; 13; 4; 10-2013; 713-722
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