arXiv research

The study proves a new inequality for strong spacelike curves in 3D Minkowski space.

The paper extends Fenchel's theorem to Lorentz space curves and proves a Crofton formula.

The paper studies pseudo-torsion functions of spacelike curves in Lorentz-Minkowski space.

Study of special vector fields on curves on spacelike surfaces.

The paper studies geometric flows of spacelike curves in Lorentz-Minkowski plane and proves their long-term behavior.

The paper studies spacelike curves and timelike ruled surfaces in Minkowski space.

The paper explores unique properties of Darboux transformations of spacelike curves in the Lorentz-Minkowski plane.

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.

In this paper, we define a rectifying spacelike curve in the Minkowski space-time $E_1^4$ as a curve whose position vector always lies in orthogonal complement $N^{\bot}$ of its principal normal vector field $N$. In particular, we study the rectifying spacelike curves in $E_1^4$ and characterize such curves in terms of…

The first aim of this paper is to define the dual timelike - spacelike Mannheim partner curves in Dual Lorentzian Space ID3 1, the second aim of this paper is to obtain the relationships between the curvatures and the torsions of the dual timelike - spacelike Mannheim partner curves with respect to each other and the f…

Study null surfaces of pseudo-spherical curves in anti-de Sitter space.

Isophote curve consists of a locus of surface points whose normal vectors make a constant angle with a fixed vector (the axis). In this paper, we define an isophote curve on a spacelike surface in Lorentz-Minkowski space and then find its axis as timelike and spacelike vectors via the Darboux frame. Besides, we give so…

The aim of this paper is to determine criteria of being integral curve for the geodesic spray of the natural lift curves of the spherical indicatrices of the involutes of a given spacelike curve with a timelike binormal in Minkowski 3-space. Furthermore, some interesting results about the spacelike evolute curve with t…

The paper studies a flow of spacelike curves in a Lorentz-Minkowski plane, showing convergence to a constant function.

In this paper, the definition of generalized spacelike Mannheim curve in Minkowski space-time $E_1^4$ is given. The necessary and sufficient conditions for the generalized spacelike Mannheim curve are obtained. Also, some characterizations of Mannheim curve are given.

The paper studies curves of constant-ratio in pseudo-Galilean space.

In this paper, we give the characterizations of spacelike B2-slant helix by means of curvatures of the spacelike curve in Minkowski 4-space. Furthermore, we give the integral characterization of the spacelike B2-slant helix.

The paper studies singularities of pedal curves of hyperbolic frontals.

Study curves in a spacelike hypersurface using geometric and singularity theory.

Extends Euler's problem to Lorentz-Minkowski plane.

In this paper, we give some characterizations for spacelike helices in Minkowski space-time. We find the differential equations characterizing the spacelike helices and also give the integral characterizations for these curves in Minkowski space-time.

Maximal Schwarzschild spacetime is inextendible with continuous metric.

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.

This paper deals with the natural lift curves and the geodesic sprays for the spherical indicatrices of the timelike-spacelike Bertrand couple on the tangent bundle or in Minkowski 3-space and then give some new characterizations for these curves. Additionally we illustrate an example of our main results.

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 …

New findings on hypersurfaces in Euclidean space that are both maximal and minimal.

In this paper we study the strong stability of spacelike hypersurfaces with constant $r$-th mean curvature in Generalized Robertson-Walker spacetimes of constant sectional curvature. In particular, we treat the case in which the ambient spacetime is the de Sitter space.

We first describe the numerical invariants attached to the second fundamental form of a spacelike surface in four-dimensional Minkowski space. We then study the configuration of the nu-principal curvature lines on a spacelike surface, when the normal field nu is lightlike (the lightcone configuration). Some observation…

Study on rotational surfaces in de Sitter space with specific curvature conditions.

Non-positively curved surfaces can be embedded in flat spacetime.

A method constructs tractor conformal bundles for spacelike submanifolds in Lorentzian manifolds.

Study on special surfaces in 4D pseudo-Euclidean space with specific Gauss maps.

Study rigidity of spacelike hypersurfaces in GRW spacetimes.

In [1], we gave a method for constructing Bertrand curves from the spherical curves in 3 dimensional Minkowski space. In this work, we construct the Bertrand curves corresponding to a spacelike geodesic and a null helix in Minkowski 4 spacetime.

Solves a Cauchy problem for minimal spacelike surfaces in 4D spacetime.

Interpolates curves using maximal and minimal surfaces in different spaces.

New Einstein-Weyl spaces derived from hyperelliptic curves.

This paper establishes an interesting connection between the family of CMC surfaces of revolution in $\mathbb E_1^3$ and some specific families of elliptic curves. As a consequence of this connection, we show in the class of spacelike CMC surfaces of revolution in the $\mathbb E_1^3$, only spacelike cylinders and stand…

The paper connects hyperbolic spinors to non-null framed curves in Minkowski 3-space.

In this paper, space and timelike admissible Smarandache curves in the pseudo- Galilean 3-space are investigated. Also, Smarandache curves of the position vector of space and timelike arbitrary curve and some of its special curves in the pseudo- Galilean 3-space are obtained. To confirm our main results, some examples …

In this paper we give necessary and sufficient conditions for spacelike and timelike curves in a conformally flat, quasi conformally flat and conformally symmetric 4-dimensional \textit{LP}-Sasakian manifold to be proper biharmonic. Also, we investigate proper biharmonic curves in the Lorentzian sphere $S^{4}_{1}$.

We review part of the classical theory of curves and surfaces in $3$-dimensional Lorentz-Minkowski space. We focus in spacelike surfaces with constant mean curvature pointing the differences and similarities with the Euclidean space.

New black hole models with both null and spacelike singularities.

The study connects curves in Anti-de Sitter space to hyperbolic plane diffeomorphisms.

In this paper we deal with curves with degeneration degree two in pseudo-Euclidean spaces of index two. We characterize Bertrand curves. We show a correspondence between the evolute of a null curve and the involute of a certain spacelike curve in the $6-$dimensional pseudo-Euclidean space of index two. Also we characte…

In this paper, we express surfaces parametrically through a given spacelike (timelike) asymptotic curve using the Frenet frame of the curve in Minkowski 3-space. Necessary and sufficient conditions for the coefficients of the Frenet frame to satisfy both parametric and asymptotic requirements are derived. We also prese…

Study of spacelike submanifolds with umbilical lightlike normals in Lorentzian spacetimes.

The strong maximum principle is proved to hold for weak (in the sense of support functions) sub- and super-solutions to a class of quasi-linear elliptic equations that includes the mean curvature equation for $C^0$ spacelike hypersurfaces in a Lorentzian manifold. As one application a Lorentzian warped product splittin…