103 citations · 175 across the 18 of their papers we have counts for
15 papers · 1 filter
Rigidity results for complete spacelike submanifolds in plane fronted waves
Francisco J. Palomo, José A. S. Pelegrín, Alfonso Romero
New rigidity results for complete non-compact spacelike submanifolds of arbitrary codimension in plane fronted waves are obtained. Under appropriate assumptions, we prove that a co…
Complete stationary spacelike surfaces in an -dimensional Generalized Robertson-Walker spacetime
Danilo Ferreira, Eraldo A. Lima, Alfonso Romero
Several uniqueness results for non-compact complete stationary spacelike surfaces in an -dimensional Generalized Robertson Walker spacetime are obtained. In order to do…
New examples of Moser-Bernstein type problems for some nonlinear elliptic partial differential equations arising in geometry
Alfonso Romero, Rafael M. Rubio, Juan J. Salamanca
A family of nonlinear partial differential equations of divergence form is considered. Each one is the Euler-Lagrange equation of a natural Riemaniann variational problem of geomet…
A new proof of a classical result on the topology of orientable connected and compact surfaces by means of the Bochner technique
J. M. Almira, A. Romero
As an application of the Bochner formula, we prove that if a -dimensional Riemannian manifold admits a non-trivial smooth tangent vector field then its Gauss curvature is th…
On uniqueness of the foliation by comoving observers restspaces of a Generalized Robertson Walker spacetime
José A. S. Pelegrín, Alfonso Romero, Rafael M. Rubio
A characterization of the foliation by spacelike slices of an -dimensional spatially closed Generalized Robertson-Walker spacetime is given by means of studying a natural me…
On the First eigenvalue of the Laplace operator for Compact Spacelike submanifolds in Lorentz-Minkowski Spacetime
Francisco J. Palomo, Alfonso Romero
By means of a family of counter-examples, it is shown that the Reilly upper bound for the first eigenvalue of the Laplace operator for a compact submanifold in Euclidean space does…
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…
Compact spacelike surfaces in four-dimensional Lorentz-Minkowski spacetime with a non-degenerate lightlike normal direction
Francisco J. Palomo, Francisco J. Rodriguez, Alfonso Romero
A spacelike surface in four-dimensional Lorentz-Minkowski spacetime through the lightcone has a meaningful lightlike normal vector field . Several sufficient assumptions on such…
Compact spacelike surfaces whose mean curvature function satisfies a nonlinear inequality in a 3-dimensional Generalized Robertson-Walker spacetime
Alfonso Romero, Rafael M. Rubio
Spacelike surfaces in Generalized Robertson-Walker spacetimes whose mean curvature function satisfies a natural nonlinear inequality are analyzed. Several uniqueness and nonexisten…
Constant mean curvature spacelike hypersurfaces in Lorentzian warped products and Calabi-Bernstein type problems
Juan A. Aledo, Alfonso Romero, Rafael M. Rubio
In this paper we provide several uniqueness and non-existence results for complete parabolic constant mean curvature spacelike hypersurfaces in Lorentzian warped products under app…
Remarks on the completeness of trajectories of accelerated particles in Riemannian manifolds and plane waves
Anna Maria Candela, Alfonso Romero, Miguel Sánchez
Recently, classical results on completeness of trajectories of Hamiltonian systems obtained at the beginning of the seventies, have been revisited, improved and applied to Lorentzi…
Completeness of trajectories of relativistic particles under stationary magnetic fields
Anna Maria Candela, Alfonso Romero, Miguel Sánchez
The second order differential equation on a Lorentzian manifold describes, in particular, the dynamics of particles und…
On spacelike surfaces in 4-dimensional Lorentz-Minkowski spacetime through a lightcone
Francisco J. Palomo, Alfonso Romero
On any spacelike surface in a lightcone of four dimensional Lorentz-Minkowski space a distinguished smooth function is considered. It is shown how both extrinsic and intrinsic geom…
Riemannian Geometry and the Fundamental Theorem of Algebra
J. M. Almira, A. Romero
If a (non-constant) polynomial has no zero, then a certain Riemannian metric is constructed on the two dimensional sphere. Several geometric arguments are then shown to contradict…