arXiv research

New submanifolds found in a specific type of space.

In this paper we study the warped product submanifolds of a Lorentzian paracosymplectic manifold and obtain some nonexistence results. We show that a warped product semi-invariant submanifold in the form {$M=M_{T}\times_{f}M_{\bot}$} of Lorentzian paracosymplectic manifold such that the characteristic vector field is n…

The paper constructs and classifies 3D Walker manifolds with specific structures.

In this paper we define and study the slant and semi-slant submanifolds of a Lorentzian almost paracontact manifold. Some necessary and sufficient conditions for a submanifold of a Lorentzian almost paracontact manifold to be slant are obtained. We give some examples for the slant and semi-slant submanifolds of a Loren…

The paper classifies 3D paracontact and almost paracosymplectic spaces.

The purpose of this paper is to study $\mathcal{P}\mathcal{R}$-semi-invariant warped product submanifolds of a paracosymplectic manifold $\widetilde{M}$. We prove that the distributions associated with the definition of $\mathcal{P}\mathcal{R}$-semi-invariant warped product submanifold $M$ are always integrable. A nece…

In this paper, we study $\mathcal{P}\mathcal{R}$-anti-slant warped product submanifold of a nearly paracosymplectic manifold $\widetilde{M}$. The necessary and sufficient condition is obtained for the distributions allied to the characterization of a $\mathcal{P}\mathcal{R}$-anti-slant submanifold being integrable and …

The paper explores Yamabe solitons on specific types of 3D manifolds.

The study examines properties of quasi-Para-Sasakian manifolds and their curvature.

This paper is a complete study of almost α-paracosmplectic manifolds. We characterize almost α-paracosmplectic manifolds which have para Kaehler leaves. Main curvature identities which are fulfilled by any almost α-paracosmplectic manifold are found. We also proved that ξ is a harmonic vector field if and only if it is…

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.

Survey of connected holonomy groups in Lorentzian manifolds.

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.

The study examines conditions for high-dimensional Lorentzian cobordisms with specific structure groups.

The study proves a transverse diameter theorem for Lorentzian foliations.

Finds a limit on Lorentzian manifolds.

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

Study submersions from Lorentzian Sasakian manifolds, finding conditions and decompositions.

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.

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

Characterizes Lorentzian manifolds embeddable in Minkowski spacetime.

Diagonalizes metrics of 3D Lorentzian manifolds.

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…

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.

Study classifies Riemann solitons on specific 3D Lorentzian groups.

Three functors link Lorentzian geometry concepts.

The Lorentzian length, which is one of the most significant functions in Lorentzian geometry, is a complex-valued function. Its square gives a real-valued non-degenerate quadratic function. In this paper, we define naturally extended mappings of Lorentzian distance-squared functions, wherein each component is a Lorentz…

Holonomy of Weyl connections in Lorentzian space classified.

Explains non-lorentzian theories and their dynamics.

The paper reconstructs Lorentzian spacetimes from causal sets.

Two flat sub-Lorentzian problems on Martinet distribution differ in attainable set intersections.

The paper studies half-lightlike submanifolds in Lorentzian manifolds with specific distributions.

Third-order symmetric Lorentzian manifolds, i.e. Lorentzian manifold with zero third derivative of the curvature tensor, are classified. These manifolds are exhausted by a special type of pp-waves, they generalize Cahen-Wallach spaces and second-order symmetric Lorentzian spaces.

The paper classifies Ricci solitons on specific Lorentzian Lie groups.

We investigate the twistor space and the Grassmannian fibre bundle of a Lorentzian 4-space with natural almost optical structures and its induced CR-structures. The twistor spaces of the Lorentzian space forms $\R^4_1, \Di{S}^4_1$ and $\Di{H}^4_1$ are explicitly discussed. The given twistor construction is applied to s…

Study finds holonomy algebras for Lorentzian Weyl spin manifolds with specific spinors.

Researchers found the longest arcs for specific sub-Lorentzian structures.