On the exponential function of an ordered manifold with affine connection.
On the Gauss curvature of maximal surfaces in the 3-dimensional Lorentz-Minkowski space.
On the Gauss image of a spacelike hypersurface with constant mean curvature in Minkowski space.
On the Gauss map of B-scrolls in -dimensional Lorentzian space forms
In this note we show that -scrolls over null curves in a 3-dimensional Lorentzian space form are characterized as the only ruled surfaces with null rulings whose Gauss maps satisfy the condition , being a parallel endomorphism of .
On the geodesic connectedeness of Lorentzian manifolds.
On the geodesic connectedness of simply connected Lorentz surfaces
On the geometric structure of the set of solutions of Einstein equations [Book]
On the geometrical properties of Heisenberg groups
In [20] the existence of major differences about totally geodesic two-dimensional foliations between Riemannian and Lorentzian geometry of the Heisenberg group is proved. Our aim in this paper is to obtain a comparison on some other geometrical properties of these spaces. Interesting behaviours are found. Also the non-existence of left-invariant Ricci and Yamabe solitons and the existence of algebraic Ricci soliton in both Riemannian and Lorentzian cases are proved. Moreover, all of the descriptions...
On the geometry of some solvable extensions of the Heisenberg group
In this paper we first classify left-invariant generalized Ricci solitons on some solvable extensions of the Heisenberg group in both Riemannian and Lorentzian cases. Then we obtain the exact form of all left-invariant unit time-like vector fields which are spatially harmonic. We also calculate the energy of an arbitrary left-invariant vector field on these spaces and obtain all vector fields which are critical points for the energy functional restricted to vector fields of the same length. Furthermore,...
On the harmonic maps from R 1,1 to S 1,1.
On the Heisenberg sub-Lorentzian metric on ℝ³
In this paper we study properties of the Heisenberg sub-Lorentzian metric on ℝ³. We compute the conjugate locus of the origin, and prove that the sub-Lorentzian distance in this case is differentiable on some open set. We also prove the existence of regular non-Hamiltonian geodesics, a phenomenon which does not occur in the sub-Riemannian case.
On the holonomy of Lorentzian metrics
Indecomposable Lorentzian holonomy algebras, except and , are not semi-simple; they possibly belong to four families of algebras. All four families are realized as families of holonomy algebras: we describe the corresponding set of germs of metrics in each case.
On the maximal spacelike submanifolds of a pseudo-Riemannian quasi constant curvature manifold.
On the quadric CMC spacelike hypersurfaces in Lorentzian space forms
We deal with complete spacelike hypersurfaces immersed with constant mean curvature in a Lorentzian space form. Under the assumption that the support functions with respect to a fixed nonzero vector are linearly related, we prove that such a hypersurface must be either totally umbilical or isometric to a hyperbolic cylinder of the ambient space.
On the Ricci operator of locally homogeneous Lorentzian 3-manifolds
We determine the admissible forms for the Ricci operator of three-dimensional locally homogeneous Lorentzian manifolds.
On the topology of spherically symmetric space-times
Spherically symmetric space-times have attained considerable attention ever since the early beginnings of the theory of general relativity. In fact, they have appeared already in the papers of K. Schwarzschild [12] and W. De Sitter [5] which were published in 1916 and 1917 respectively soon after Einstein's epoch-making work [7] in 1915. The present survey is concerned mainly with recent results pertainig to the toplogy of spherically symmetric space-times. Definition. By space-time a connected...
On the twistor bundle of de Sitter space .
On the wave equation in curved spacetime
Osculating curves in 4-dimensional semi-Euclidean space with index 2
In this paper, we give the necessary and sufficient conditions for non-null curves with non-null normals in 4-dimensional Semi-Euclidian space with indeks 2 to be osculating curves. Also we give some examples of non-null osculating curves in [...] E24 .
Parabolicity and rigidity of spacelike hypersurfaces immersed in a Lorentzian Killing warped product
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.