We establish the links between lightlike geometry and basics invariants of associated semi-Riemannian on r-lightlike submanifold constructed from a ambient. Then we some basic inequalities, involving scalar curvature shape operator coisotropic in manifold. Equality cases are also discussed.

We obtain the expression of Ricci tensor for a $GCR$-lightlikesubmanifold of indefinite complex space form and discuss itsproperties on a totally geodesic $GCR$-lightlike submanifold of anindefinite complex space form. Moreover, we have proved that everyproper totally umbilical $GCR$-lightlike submanifold of anindefinite Kaehler manifold is a totally geodesic $GCR$-lightlikesubmanifold.

We introduce the geometry of pseudo-totally umbilical lightlike submanifold $M$ a semi-Riemannian manifold $\bar{M}$. In line with above, we give complete classification $1$-lightlike submanifolds, such as hypersurfaces and half-lightlike submanifolds. Furthermore, screen distributions are also investigated, for any whose umbilical. Closely linked to above show, under some geometric conditions,...

The oriented angles between lightlike vectors cannot be defined properly compared to the timelike in Minkowski spacetime. Therefore, we use pseudo-angles any non-lightlike or develop theory of surfaces having constant angle with a fixed nonlightlike direction. We investigate some geometric properties on these such as being tangent developable. Besides, construct ruled by means null helices. giv...

We consider dimensional reduction of the lightlike holography of the covariant entropy bound from D + 1 dimensional geometry of M × S1 to the D dimensional geometry M . With a warping factor, the local Bekenstein bound in D+ 1 dimensions leads to a more refined form of the bound from the D dimensional view point. With this new local Bekenstein bound, it is quite possible to saturate the lightli...

Massless elementary-particle propagation is represented historically (cosmologically) through 3-scale “towers of quartet rings” within a lattice of magneto-electrodynamically communicating “pre-events”. The lightlike intervals within a ring of 4 pre-events (discrete “closed string”) display transverse GUT-scale and longitudinal “particle scale”. The lightlike (longitudinal) spacing between succ...

In this paper, firstly, in $E_1^3$, we defined normal Fermi-Walker derivative and applied for the adapted frame. Normal Fermi-Walker parallelism, normal non-rotating frame, and Darboux vector expressions of normal Fermi-Walker derivative by normal Fermi-Walker derivative are given for adapted frame. Being conditions of normal Fermi-Walker derivative and normal non-rotating frame are examined fo...

∇XV = λX for every vector field X. (1.2) Here ∇ denotes the Levi-Civita connection of g. We call vector fields satisfying (1.2) closed conformal vector fields. They appear in the work of Fialkow [3] about conformal geodesics, in the works of Yano [7–11] about concircular geometry in Riemannian manifolds, and in the works of Tashiro [6], Kerbrat [4], Kühnel and Rademacher [5], and many other aut...

We investigate Kaluza-Klein metrics with a recurrent lightlike vector field over a pseudo-Riemannian manifold (B, g).