The magnetic flow on the manifold of oriented geodesics of a three dimensional space form
Let M be the three dimensional complete simply connected manifold of constant sectional curvature 0,10,1 or −1−1. Let L be the manifold of all (unparametrized) complete oriented geodesics of M, endowed with its canonical pseudo-Riemannian metric of signature (2,2)(2,2) and Kähler structure J. A smoo...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2013 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/8984 |
| Acceso en línea: | http://hdl.handle.net/11336/8984 |
| Access Level: | acceso abierto |
| Palabra clave: | MANIFOLD OF ORIENTED GEODESICS HERMITIAN SYMMETRIC SPACE MAGNETIC FLOW RULED SURFACE HOROSPHERICAL DISTRIBUTION https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | Let M be the three dimensional complete simply connected manifold of constant sectional curvature 0,10,1 or −1−1. Let L be the manifold of all (unparametrized) complete oriented geodesics of M, endowed with its canonical pseudo-Riemannian metric of signature (2,2)(2,2) and Kähler structure J. A smooth curve in L determines a ruled surface in M. We characterize the ruled surfaces of MM associated with the magnetic geodesics of LL, that is, those curves σσ in LL satisfying ∇σ˙σ˙=Jσ˙∇σ˙σ˙=Jσ˙. More precisely: a time-like (space-like) magnetic geodesic determines the ruled surface in M given by the binormal vector field along a helix with positive (negative) torsion. Null magnetic geodesics describe cones, cylinders or, in the hyperbolic case, also cones with vertices at infinity. This provides a relationship between the geometries of L and M. |
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