5 papers
Uniqueness and non-existence of minimal submanifolds
R. M. Rubio, J. J. Salamanca
We provide uniqueness results for compact minimal submanifolds in a large class of Riemannian manifolds of arbitrary dimension. In the case compact and Cartan-Hadamard manifolds we…
Uniqueness of complete maximal hypersurfaces in spatially open -dimensional Robertson-Walker spacetimes with flat fiber
José A. S. Pelegrín, Alfonso Romero, Rafael M. Rubio
In this paper, under natural geometric and physical assumptions we provide new uniqueness and non-existence results for complete maximal hypersurfaces in spatially open Robertson-W…
On maximal hypersurfaces in Lorentz manifolds admitting a parallel lightlike vector field
José A. S. Pelegrín, Alfonso Romero, Rafael M. Rubio
We study constant mean curvature spacelike hypersurfaces and in particular maximal hypersurfaces immersed in pp-wave spacetimes satisfying the timelike convergence condition. We pr…
A dual rigidity of the sphere and the hyperbolic plane
Magdalena Caballero, Rafael M. Rubio
There are several well-known characterizations of the sphere as a regular surface in the Euclidean space. By means of a purely synthetic technique, we get a rigidity result for the…
Complete Spacelike Hypersurfaces in Generalized Robertson-Walker and the Null Convergence Condition. Calabi-Bernstein problems
Juan A. Aledo, Rafael M. Rubio, Juan J. Salamanca
We study constant mean curvature spacelike hypersurfaces in generalized Robertson-Walker spacetimes which are spatially parabolic covered (i.e. its fiber F is a (non- compact) comp…