Homogeneous hypersurfaces in symmetric spaces
A hypersurface of a Riemannian manifold is called homogeneous if it is an orbit of an isometric action on the ambient manifold. Homogeneous hypersurfaces have remarkable geometric properties, providing the simplest examples of hypersurfaces with constant mean curvature. Thus, they are crucial for th...
| Autores: | , , |
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| Tipo de recurso: | capítulo de libro |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universidad de Santiago de Compostela (USC) |
| Repositorio: | Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela |
| Idioma: | inglés |
| OAI Identifier: | oai:minerva.usc.gal:10347/44120 |
| Acceso en línea: | https://hdl.handle.net/10347/44120 |
| Access Level: | acceso abierto |
| Palabra clave: | Symmetric space noncompact type homogeneous submanifold isometric action cohomogeneity one action isoparametric hypersurface minimal submanifold constant principal curvatures projective space hyperbolic space parabolic subgroup |
| Sumario: | A hypersurface of a Riemannian manifold is called homogeneous if it is an orbit of an isometric action on the ambient manifold. Homogeneous hypersurfaces have remarkable geometric properties, providing the simplest examples of hypersurfaces with constant mean curvature. Thus, they are crucial for the investigation of more general types of submanifolds in ambient spaces with large isometry groups. In this survey article we present an introduction to some of the basic geometric, topological, and algebraic features of homogeneous hypersurfaces, describing what is known about their classification problem in symmetric spaces, and explaining the main tools needed for their study in the context of symmetric spaces of noncompact type. |
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