Kinematics of relative motion of test particles in general relativity
Krümmungstreue Diffeomorphismen Riemannscher und pseudo-Riemannscher Mannigfaltigkeiten.
Lightlike ruled surfaces in .
Lorentzian geometry as determined by the volumes of small truncated light cones
Matter field space times admitting symmetry mappings satisfying vanishing contraction of the Lie deformation of the Ricci tensor
Metric of special 2F-flat Riemannian spaces
In this paper we find the metric in an explicit shape of special -flat Riemannian spaces , i.e. spaces, which are -planar mapped on flat spaces. In this case it is supposed, that is the cubic structure: .
Minimal lightlike hypersurfaces in with integrable screen distribution.
Minkowski asymptotic spaces in general relativity
Minkowski minimal surfaces in with minimal focal surfaces.
New characterizations of linear Weingarten hypersurfaces immersed in the hyperbolic space
In this paper, we deal with complete linear Weingarten hypersurfaces immersed in the hyperbolic space , that is, complete hypersurfaces of whose mean curvature and normalized scalar curvature satisfy for some , . In this setting, under appropriate restrictions on the mean curvature and on the norm of the traceless part of the second fundamental form, we prove that such a hypersurface must be either totally umbilical or isometric to a hyperbolic cylinder of . Furthermore, a rigidity result...
Newton transformations on null hypersurfaces
Any rigged null hypersurface is provided with two shape operators: with respect to the rigging and the rigged vector fields respectively. The present paper deals with the Newton transformations built on both of them and establishes related curvature properties. The laters are used to derive necessary and sufficient conditions for higher-order umbilicity and maximality we introduced in passing, and develop general Minkowski-type formulas for the null hypersurface, supported by some physical models...
Non-degenerate hypersurfaces of a semi-Riemannian manifold with a semi-symmetric metric connection
We derive the equations of Gauss and Weingarten for a non-degenerate hypersurface of a semi-Riemannian manifold admitting a semi-symmetric metric connection, and give some corollaries of these equations. In addition, we obtain the equations of Gauss curvature and Codazzi-Mainardi for this non-degenerate hypersurface and give a relation between the Ricci and the scalar curvatures of a semi-Riemannian manifold and of its a non-degenerate hypersurface with respect to a semi-symmetric metric connection....
Null cones and pseudo-riemannian metrics.
Null generalized helices in .
Null scrolls in the 3-dimensional Lorentzian space.
On a Certain Extension of the Class of Semisymmetric Manifolds
On a Class of Generalized quasi-Einstein Manifolds with Applications to Relativity
Quasi Einstein manifold is a simple and natural generalization of Einstein manifold. The object of the present paper is to study some properties of generalized quasi Einstein manifolds. We also discuss with space-matter tensor and some properties related to it. Two non-trivial examples have been constructed to prove the existence of generalized quasi Einstein spacetimes.
On a class of Ricci-recurrent manifolds.
On a conjecture about the Gauss map of complete spacelike surfaces with constant mean curvature in the Lorentz-Minkowski space.
On a Theorem of Chern and Terng on Affine Surfaces.