Rigidity of pseudo-isotropic immersions
|Author/s||Cabrerizo Jaraíz, José Luis
Fernández Andrés, Manuel
Gómez Casanueva, Juan Salvador
|Department||Universidad de Sevilla. Departamento de Geometría y Topología|
|Abstract||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 ...
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.
|Citation||Cabrerizo Jaraíz, J.L., Fernández Andrés, M. y Gómez Casanueva, J.S. (2009). Rigidity of pseudo-isotropic immersions. Journal of Geometry and Physics, 59 (7), 834-842.|