Rigidity of pseudo-isotropic immersions
Several notions of isotropy of a (pseudo)Riemannian manifold have been introduced in the literature, in particular, the concept of pseudo-isotropic immersion. The aim of this paper is to look more closely at this notion of pseudoisotropy and then to study the rigidity of this class of immersion into...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2009 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/47729 |
| Acceso en línea: | http://hdl.handle.net/11441/47729 https://doi.org/10.1016/j.geomphys.2009.03.006 |
| Access Level: | acceso abierto |
| Palabra clave: | Pseudo-Riemannian manifold Isotropic immersion Pseudoisotropic submanifold Rigid immersion |
| Sumario: | Several notions of isotropy of a (pseudo)Riemannian manifold have been introduced in the literature, in particular, the concept of pseudo-isotropic immersion. The aim of this paper is to look more closely at this notion of pseudoisotropy and then to study the rigidity of this class of immersion into the pseudo-Euclidean space. It is worth pointing out that we first obtain a characterization of the pseudo-isotropy condition by using tangent vectors of any causal character. Then, rigidity theorems for pseudo-isotropic immersions are proved, and in particular, some well known results for the Riemannian case arise. Later, we bring together the notions of pseudo-isotropy, intrinsically and extrinsically isotropic manifolds, and prove interesting relations among them. Finally, we pay special attention to the case of codimension two Lorentz surfaces. |
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