arXiv research

Introduces new lightlike submanifolds in indefinite Kaehler manifolds.

Study lightlike submanifolds in indefinite statistical manifolds, finding conditions and curvature expressions.

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

Study the geometry of specific submanifolds in Golden Semi-Riemannian manifolds.

Study on lightlike submanifolds in statistical manifold geometry.

Study on lightlike submanifolds in metallic semi-Riemannian manifolds.

Study on SASI-lightlike submanifolds in indefinite Kaehler manifolds.

Study on CR-lightlike submanifolds in golden semi-Riemannian manifolds.

The paper studies lightlike submanifolds in bronze semi-Riemannian manifolds with specific geometric properties.

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

Study lightlike submanifolds in Golden Semi-Riemannian geometry.

In this paper, we introduce and study a new class of CR-lightlike submanifold of an indefinite nearly Sasakian manifold, called Quasi Generalized Cauchy-Riemann (QGCR) lightlike submanifold. We give some characterization theorems for the existence of QGCR-lightlike submanifolds and finally derive necessary and sufficie…

Study the geometry of transversal lightlike submanifolds in Metallic Semi-Riemannian manifolds.

We investigate half-lightlike submanifolds with planar normal sections of four dimensional pseudo Euclidean space. We obtain necessary and sufficient conditions for a half-lightlike submanifold of $R_{2}^{4}$ such that it has degenerate or non-degenerate planar normal sections.

Study on a new type of submanifolds in geometric spaces.

In this paper, we study Jacobi operators associated to algebraic curvature maps (tensors) on lightlike submanifolds M. We investigate conditions for an induced Rie- mann curvature tensor to be an algebraic curvature tensor on M. We introduce the notion of lightlike Osserman submanifolds and an example of 2-degenerate O…

The concept of quasi generalized CR-lightlike was first introduced by the authors in [18]. In this paper, we focus on ascreen and co-screen quasi generalized CR-lightlike submanifolds of indefinite nearly $μ$-Sasakian manifold. We prove an existence theorem for minimal ascreen quasi generalized CR-lightlike submanifold…

Study on lightlike geometry in indefinite Sasakian statistical manifolds.

Anti-de Sitter space is the Lorentzian space form with negative curvature. In this paper we consider lightlike hypersurfaces along spacelike submanifolds in anti-de Sitter space with general codimension. In particular, we investigate the singularities of lightlike hypersurfaces as an application of the theory of Legend…

We derive total mean curvature integration formulae of a three co-dimensional foliation $\mathcal{F}^{n}$ on a screen integrable half-lightlike submanifold, $M^{n+1}$ in a semi-Riemannian manifold $\overline{M}^{n+3}$. We give generalized differential equations relating to mean curvatures of a totally umbilical half-li…

In this paper we study submanifolds of an almost complex manifold with Norden metric which are non-degenerate with respect to the one Norden metric and lightlike with respect to the other Norden metric on the manifold. Relations between the induced geometric objects of some of these submanifolds are given. Examples of …

Study on umbilical submanifolds in specific geometric spaces.

Study finds rigid submanifolds in spacelike waves under specific conditions.

Study on spacelike submanifolds in generalized Schwarzschild spacetimes with lightlike foliations.

Study characterizes submanifolds in metallic semi-Riemannian manifolds with specific connections.

We introduce higher order mean curvatures of screen almost conformal (SAC) half-lightlike submanifolds of indefinite contact manifolds, admitting a semi-symmetric non-metric connection, and use them to generalize some known results of [6]. Also, we derive a new set of integration formulae via the divergence of some spe…

A world sheet in anti-de Sitter space is a timelike submanifold consisting of a one-parameter family of spacelike submanifolds. We consider the family of lightlike hypersurfaces along spacelike submanifolds in the world sheet. The locus of the singularities of lightlike hypersurfaces along spacelike submanifolds forms …

The authors study the geometry of lightlike hypersurfaces on manifolds $(M, c)$ endowed with a pseudoconformal structure $c = CO (n - 1, 1)$ of Lorentzian signature. Such hypersurfaces are of interest in general relativity since they can be models of different types of physical horizons. On a lightlike hypersurface, th…

The lightlike geometry of codimension two spacelike submanifolds in Lorentz-Minkowski space has been developed in [Izumiya, S. and Romero Fuster, M. C. Selecta Mathematica (NS), 13 23--55 (2007)] which is a natural Lorentzian analogue of the classical Euclidean differential geometry of hypersurfaces. In this paper we i…

The authors study the geometry of lightlike hypersurfaces on a four-dimensional manifold $(M, c)$ endowed with a pseudoconformal structure $c = CO (2, 2)$. They prove that a lightlike hypersurface $V \subset (M, c)$ bears a foliation formed by conformally invariant isotropic geodesics and two isotropic distributions ta…

We introduce the totally absolute lightcone curvature for a spacelike submanifold with general codimension and investigate global properties of this curvature. One of the consequences is that the Chern-Lashof type inequality holds. Then the notion of lightlike tightness is naturally induced.

Degenerate submanifolds of pseudo-Riemannian manifolds are quite difficult to study because there is no prefered connection when the submanifold is not totally geodesic. For the particular case of degenerate totally umbilical hypersurfaces, we show that there are "Weyl" connections adapted to the induced structure on t…

Mixed 3-structures are odd-dimensional analogues of paraquaternionic structures. They appear naturally on lightlike hypersurfaces of almost paraquaternionic hermitian manifolds. We study invariant and anti-invariant submanifolds in a manifold endowed with a mixed 3-structure and a compatible (semi-Riemannian) metric. P…

Study submanifolds in null hypersurfaces of generalized Robertson-Walker spacetimes.

The authors study the geometry of lightlike hypersurfaces on pseudo-Riemannian manifolds $(M, g)$ of Lorentzian signature. Such hypersurfaces are of interest in general relativity since they can be models of different types of physical horizons. For a lightlike hypersurface $V \subset (M, g)$ of general type and for so…

Study geometric properties of SGL submanifolds in a specific manifold.

There are three types of hypersurfaces in a pseudoconformal space C^n_1 of Lorentzian signature: spacelike, timelike, and lightlike. These three types of hypersurfaces are considered in parallel. Spacelike hypersurfaces are endowed with a proper conformal structure, and timelike hypersurfaces are endowed with a conform…

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

An important, if relatively less well known aspect of the singularity theorems in Lorentzian Geometry is to understand how their conclusions fare upon weakening or suppression of one or more of their hypotheses. Then, theorems with modified concusions may arise, showing that those conclusions will fail only in special …

Study the geometry of lightlike loci on mixed type surfaces in Lorentz-Minkowski 3-space.

Lightlike manifolds studied via Cartan geometries in Lorentz-Minkowski spacetime.

Study on lightlike hypersurfaces in metallic semi-Riemannian manifolds.

Constructs Lorentzian manifolds from Riemannian conformal structures.

Lightlike hypersurfaces in statistical manifolds have unique geometric properties.

In this paper we study lightlike surfaces of Minkowski 3- space such that they have degenerate or non-degenerate planar normal sections. We first show that every lightlike surface of Minkowski $3-$ space has degenerate planar normal sections. Then we study lightlike surfaces with non-degenerate planar normal sections a…

This paper studies lightlike Cartan geometries and their properties.

In this paper, we initiate the study of lightlike hypersurfaces of an $(ε)$-almost paracontact metric manifold which are tangent to the structure vector field. In particular, we give definitions of invariant lightlike hypersurfaces and screen semi-invariant lightlike hypersurfaces, and give some examples. Integrability…

Study on Dirac operators on lightlike hypersurfaces in 4D Lorentzian manifolds.