arXiv research

Defines Lorentzian angles for null vectors in geometry.

In Lorentzian geometry, limited definition of angles restricts the use of angle bisectors in study of triangles. This paper redefines angle bisectors so that they can be used to study attributes of triangles. Using the new definition, this paper investigates the existence of the incenter and the isogonal conjugate of a…

Study on null hypersurfaces with constant angle in Lorentzian manifolds.

The study introduces hyperbolic angles in Lorentzian spaces and characterizes curvature bounds.

Study classifies helix surfaces in Lorentzian Heisenberg group.

In this paper, we define and, then, we characterize constant angle spacelike and timelike surfaces in the three-dimensional Heisenberg group, equipped with a 1-parameter family of Lorentzian metrics. In particular, we give an explicit local parametrization of these surfaces and we produce some examples.

In this paper, we investigate the relations between the pitch, the angle of pitch and drall of parallel ruled surface of a closed curve in dual Lorentzian space.

Study on Lorentzian spaces with curvature bounds, proving comparison theorems.

In this paper we study slant submanifolds of Lorentzian almost contact manifolds. We have taken the submanifold as a space like and then defined the slant angle on a submanifold and thus we extended the results of A. Lotta (Slant submanifolds in contact geometry [8]) and M. A. Khan et. al. (Slant submanifolds of Lorent…

In this paper, we investigate the relations between the pitch, the angle of pitch and drall of parallel ruled surface of a closed spacelike curve with timelike binormal in dual Lorentzian space.

In this paper, we investigate the relations between the pitch, the angle of pitch and drall of parallel ruled surface of a closed spacelike curve with a spacelike binormal in dual Lorentzian space.

We first define a complex angle between two oriented spacelike planes in 4-dimensional Minkowski space, and then study the constant angle surfaces in that space, i.e. the oriented spacelike surfaces whose tangent planes form a constant complex angle with respect to a fixed spacelike plane. This notion is the natural Lo…

In this work, we study helix spacelike and timelike surfaces in the Lorentzian Berger sphere $\s_{\varepsilon}^3$, that is the three-dimensional sphere endowed with a $1$-parameter family of Lorentzian metrics, obtained by deforming the round metric on $\s^3$ along the fibers of the Hopf fibration $\s^3\to \s^2({1}/{2}…

Paper proves rigidity of de-Sitter tori with conical singularities.

In this paper, we define dual geodesic trihedron(dual Darboux frame) of a spacelike ruled surface. Then, we study Mannheim offsets of spacelike ruled surfaces in dual Lorentzian space by considering the E. Study Mapping. We represent spacelike ruled surfaces by dual Lorentzian unit spherical curves and define Mannheim …

Synthetic approach to conformal transformations in metric and Lorentzian spaces.

Study laws of cosines and sines for hyperbolic shapes with ideal vertices.

We consider compact hypersurfaces in an $(n+1)$-dimensional either Riemannian or Lorentzian space $N^{n+1}$ endowed with a conformal Killing vector field. For such hypersurfaces, we establish an integral formula which, especially in the simpler case when $N=M^n\times R$ is a product space, allows us to derive some inte…

The aim of this paper is to present a new perspective on the generation of developable trajectory ruled surfaces in Minkowski 3-space. Involute trajectory ruled surfaces generated by the Frenet trihedron, moving along spacelike involutes of a given timelike space curve, is stated according to Lorentzian timelike angle …

In this paper, we classify all the orientable hyperbolic 5-manifolds that arise as a hyperbolic space form $H^5/Γ$ where $Γ$ is a torsion-free subgroup of minimal index of the congruence two subgroup $Γ^5_2$ of the group $Γ^5$ of positive units of the Lorentzian quadratic form $x_1^2+...+x_5^2-x_6^2$. We also show that…

New method proves Alexandrov theorem for curved spacetimes.

Using global considerations, Mess proved that the moduli space of globally hyperbolic flat Lorentzian structures on $S\times\mathbb{R}$ is the tangent bundle of the Teichmüller space of $S$, if $S$ is a closed surface. One of the goals of this paper is to deepen this surprising occurrence and to make explicit the relat…

In this work we study spacelike hypersurfaces immersed in spatially open standard static spacetimes with complete spacelike slices. Under appropriate lower bounds on the Ricci curvature of the spacetime in directions tangent to the slices, we prove that every complete CMC hypersurface having either bounded hyperbolic a…

In this article we study minimal flat Lorentzian surfaces in Lorentzian complex space forms. First we prove that, for minimal flat Lorentzian surfaces in a Lorentzian complex form, the equation of Ricci is a consequence of the equations of Gauss and Codazzi. Then we classify minimal flat Lorentzian surfaces in the Lore…

Defines metrics for Lorentzian spaces and explores maximal developments.

Study of a series of Lorentzian structures on SL(2,R) with SO(1,1) symmetry.

Study left-invariant Codazzi tensors and harmonic curvature on Lorentzian Lie groups.

It is shown how one can apply the classification of the holonomy algebras of Lorentzian manifolds to solve some problems. In particular, a new proof to the classification of Lorentzian manifolds with recurrent curvature tensor is given; the classification of two-symmetric Lorentzian manifolds is explained; conformally …

Study gluing of Lorentzian length spaces and their causal ladder properties.

Defines doubling conditions for Lorentzian spaces linked to curvature bounds.

Research explores Lorentzian distances on a specific geometric plane.

Finds a limit on Lorentzian manifolds.

The study proves a transverse diameter theorem for Lorentzian foliations.

The paper classifies 3D Lorentzian $Ein(2)$ Lie groups.

Timelike minimal surfaces in Lorentzian Heisenberg group have singular points.

Study of 2D Lorentzian anti-de Sitter plane using geometric control theory.

Defines new metrics for Lorentzian spaces and their convergence.

Compact group found for special Lorentzian manifolds.

Characterizes Lorentzian manifolds embeddable in Minkowski spacetime.

Diagonalizes metrics of 3D Lorentzian manifolds.

We give the global mathematical formulation of a class of generalized four-dimensional theories of gravity coupled to scalar matter and to Abelian gauge fields. In such theories, the scalar fields are described by a section of a surjective pseudo-Riemannian submersion $π$ over space-time, whose total space carries a Lo…

We study necessary and sufficient conditions for the existence of Lorentzian and weak Lorentzian cobordisms between closed smooth manifolds of arbitrary dimension such that the structure group of the frame bundle of the cobordism is $\Spin(1, n)_0$. This extends a result of Gibbons-Hawking on $\Sl(2, \C)$-Lorentzian co…

Proves a synthetic Lorentzian Cartan-Hadamard theorem.

In this paper, we study the invariant and noninvariant hypersurfaces of (1,1,1) almost contact manifolds, Lorentzian almost paracontact manifolds and Lorentzian para-Sasakian manifolds, respectively. We show that a noninvariant hypersurface of an (1,1,1) almost contact manifold admits an almost product structure. We in…

Study classifies Riemann solitons on specific 3D Lorentzian groups.

If an $m+2$-manifold $M$ is locally modeled on $\RR^{m+2}$ with coordinate changes lying in the subgroup $G=\RR^{m+2}\rtimes ({\rO}(m+1,1)\times \RR^+)$ of the affine group ${\rA}(m+2)$, then $M$ is said to be a \emph{Lorentzian similarity manifold}. A Lorentzian similarity manifold is also a conformally flat Lorentzia…

Proves existence of longest paths in sub-Lorentzian problems.

Three functors link Lorentzian geometry concepts.