The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
In this paper, we extend a technique due to Romero et al. establishing sufficient conditions to guarantee the parabolicity of complete spacelike hypersurfaces immersed into a Lorentzian Killing warped product whose Riemannian base has parabolic universal Riemannian covering. As applications, we obtain rigidity results concerning these hypersurfaces. A particular study of entire Killing graphs is also made.
In this paper we study parallel and totally geodesic hypersurfaces of two-step homogeneous nilmanifolds of dimension five. We give the complete classification and explicitly describe parallel and totally geodesic hypersurfaces of these spaces. Moreover, we prove that two-step homogeneous nilmanifolds of dimension five which have one-dimensional centre never admit parallel hypersurfaces. Also we prove that the only two-step homogeneous nilmanifolds of dimension five which admit totally geodesic hypersurfaces...
In this paper we consider special examples of homogeneous spaces of arbitrary odd dimension which are given in [5] and [16]. We obtain the complete classification and explicitly describe parallel and totally geodesic hypersurfaces of these spaces in both Riemannian and Lorentzian cases.
We investigate parallel hypersurfaces in the context of relative hypersurface geometry, in particular including the cases of Euclidean and Blaschke hypersurfaces. We describe the geometric relations between parallel hypersurfaces in terms of deformation operators, and we apply the results to the parallel deformation of special classes of hypersurfaces, e.g. quadrics and Weingarten hypersurfaces.
Let be a Riemann surface. Let be the -dimensional hyperbolic space and let be its ideal boundary. In our context, a Plateau problem is a locally holomorphic mapping . If is a convex immersion, and if is its exterior normal vector field, we define the Gauss lifting, , of by . Let be the Gauss-Minkowski mapping. A solution to the Plateau problem is a convex immersion of constant Gaussian curvature equal to such that the Gauss lifting is complete and . In this paper, we show...
We study the existence of surfaces with constant or prescribed Gauss curvature in certain Lorentzian spacetimes. We prove in particular that every (non-elementary) 3-dimensional maximal globally hyperbolic spatially compact spacetime with constant non-negative curvature is foliated by compact spacelike surfaces with constant Gauss curvature. In the constant negative curvature case, such a foliation exists outside the convex core. The existence of these foliations, together with a theorem of C. Gerhardt,...
Currently displaying 1 –
20 of
21