Calibrated geodesic foliations of hyperbolic space
Let H be the hyperbolic space of dimension n + 1. A geodesic foliation of H is given by a smooth unit vector field on L all of whose integral curves are geodesics. Each geodesic foliation of L determines an n-dimensional submanifold of the 2n-dimensional manifold L of all the oriented geodesics of H...
| Autores: | , |
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| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2016 |
| País: | Argentina |
| Recursos: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/58362 |
| Acesso em linha: | http://hdl.handle.net/11336/58362 |
| Access Level: | acceso abierto |
| Palavra-chave: | GEODESIC FOLIATION HYPERBOLIC SPACE SPACE OF GEODESICS SPLIT SPECIAL LAGRANGIAN CALIBRATION https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Resumo: | Let H be the hyperbolic space of dimension n + 1. A geodesic foliation of H is given by a smooth unit vector field on L all of whose integral curves are geodesics. Each geodesic foliation of L determines an n-dimensional submanifold of the 2n-dimensional manifold L of all the oriented geodesics of H (up to orientation preserving reparametrizations). The space L has a canonical split semi-Riemannian metric induced by the Killing form of the isometry group of L. Using a split special Lagrangian calibration, we study the volume maximization problem for a certain class of geometrically distinguished geodesic foliations, whose corresponding submanifolds of L are space-like. |
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