Half Lightlike Submanifolds Research Articles

Half Lightlike Submanifolds of A Golden Semi-Riemannian Manifold

We present half lightlike submanifolds of a golden semi-Riemannian manifold. We prove that there is no radical anti-invariant half lightlike submanifold of a golden semi-Riemannian manifold. We get results for screen semi-invariant half lightlike submanifolds of a golden semi-Riemannian manifold. We prove the conditions for integrability of distributions on screen semi-invariant half lightlike submanifolds and investigate the geometry of leaves of distributions. Moreover, we study screen conformal half lightlike submanifolds of a golden semi-Riemannian manifold.

Half-Lightlike Submanifolds of Metallic semi-Riemannian Manifolds

The aim of the present paper is to study half-lightlike submanifolds of a semi-Riemannian manifold endowed with a metallic structure. We introduce a special half-lightlike submanifold called screen semi-invariant half lightlike submanifold in metallic semi-Riemannian manifolds and give an example. We present necessary and sufficient conditions for the distributions included in the definition of such half lightlike submanifolds to be integrable. Moreover, we analyze geometry of a screen semi-invariant half lightlike submanifold in a locally metallic semi- Riemannian manifold when it is totally geodesic and screen conformal.

Half lightlike submanifolds of an indefinite trans-Sasakian manifold with a non-metric $$\phi $$-symmetric connection

Half lightlike submanifolds of an indefinite trans-Sasakian manifold with a non-metric $$\phi $$-symmetric connection

Some Inequalities on Half Lightlike Submanifolds of a Lorentzian Manifold with Semi-Symmetric Metric Connection

In this paper, we introduce some inequalities for screen homothetic half lightlike submanifolds of a real space form of constant sectional curvature , endowed with semi-symmetric metric connection. Using these inequalities, we derive some characterizations for such half lightlike submanifolds. Finally, Chen-Ricci inequalities are calculated. Morever, the equality cases are considered and we get some results.

A Study on Chen-like Inequalities for Half Lightlike Submanifolds of a Lorentzian Manifold Endowed with Semi-Symmetric Metric Connection

In this paper, Chen-like inequalities of a half lightlike submanifolds of a real space form N(c) with constant sectional curvature c, equipped with semi-symmetric metric connection are established and some important characterization theorems for such submanifolds are proved using these inequalities.

On total mean curvatures of foliated half-lightlike submanifolds in semi-Riemannian manifolds

We derive total mean curvature integration formulas 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-lightlike submanifold admitting a totally umbilical screen distribution, and show that they are generalizations of those given by [K. L. Duggal and B. Sahin, Differential geometry of lightlike submanifolds, Frontiers in Mathematics, Birkhäuser Verlag, Basel, 2010].

Higher order mean curvatures of SAC half-lightlike submanifolds of indefinite almost contact manifolds

We introduce higher order mean curvatures of screen almost conformal (SAC) half-lightlike submanifolds of indefinite almost contact manifolds, admitting a semi-symmetric non-metric connection. We use them to generalize some known results by Duggal and Sahin on totally umbilical half-lightlike submanifolds [Int. J. Math. Math. Sci. 2004, no. 68, 3737-3753]. Also, we derive a new integration formula via the divergence of some special vector fields tangent to these submanifolds, which we later use to characterize minimal and maximal submanifolds. Several examples, where possible, are also included to illustrate the main concepts.

HALF LIGHTLIKE SUBMANIFOLDS OF AN INDEFINITE KAEHLER MANIFOLD WITH A SEMI-SYMMETRIC NON-METRIC CONNECTION

In this paper, we study half lightlike submanifolds of an indefinite Kaehler manifold with a semi-symmetric non-metric connection. First, we characterize the geometry of two types of half lightlike submanifolds of such an indefinite Kaehler manifold. Next, we investigate the geometry of half lightlike submanifolds of an indefinite complex space form with a semi-symmetric non-metric connection.

STATICAL HALF LIGHTLIKE SUBMANIFOLDS OF AN INDEFINITE KAEHLER MANIFOLD OF A QUASI-CONSTANT CURVATURE

In this paper, we study half lightlike submanifolds M of an indefinite Kaehler manifold <TEX>$\bar{M}$</TEX> of quasi-constant curvature such that the characteristic vector field <TEX>${\zeta}$</TEX> of <TEX>$\bar{M}$</TEX> is tangent to M. First, we provide a new result for such a half lightlike submanifold. Next, we investigate a statical half lightlike submanifold M of <TEX>$\bar{M}$</TEX> subject such that (1) the screen distribution S(TM) is totally umbilical or (2) M is screen conformal.

TRANSVERSAL HALF LIGHTLIKE SUBMANIFOLDS OF AN INDEFINITE KAEHLER MANIFOLD OF A QUASI-CONSTANT CURVATURE

We study transversal half lightlike submanifolds of an indefinite Kaehler manifold of a quasi-constant curvature. First, we provide a new result for such a transversal half lightlike submanifold. Next, we investigate a statical half lightlike submanifold M such that (1) the screen distribution S(TM) is totally umbilical, or (2) M is screen homothetic.

Half lightlike submanifolds of a semi-Riemannian manifold of quasi-constant curvature

We study the geometry of half lightlike submanifolds (M,g,S(TM), S(TM?)) of a semi-Riemannian manifold (M~,g~) of quasi-constant curvature subject to the following conditions; (1) the curvature vector field ? of M~ is tangent to M, (2) the screen distribution S(TM) of M is either totally geodesic or totally umbilical in M, and (3) the co-screen distribution S(TM?) of M is a conformal Killing distribution.

Half lightlike submanifolds of a trans-Sasakian manifold with a semi-symmetric non-metric connection

Half lightlike submanifolds of a trans-Sasakian manifold with a semi-symmetric non-metric connection

NON-EXISTENCE FOR SCREEN QUASI-CONFORMAL IRROTATIONAL HALF LIGHTLIKE SUBMANIFOLDS OF A SEMI-RIEMANNIAN SPACE FORM ADMITTING A SEMI-SYMMETRIC NON-METRIC CONNECTION

We study screen quasi-conformal irrotational half lightlike submanifolds M of a semi-Riemannian space form (c) equipped with a semi-symmetric non-metric connection subject such that the structure vector field of (c) belongs to the screen distribution S(TM). The main result is a non-existence theorem for such half lightlike submanifolds.

HALF LIGHTLIKE SUBMANIFOLDS OF AN INDEFINITE TRANS-SASAKIAN MANIFOLD OF QUASI-CONSTANT CURVATURE

We study half lightlike submanifolds M of an indefinite trans-Sasakian manifold <graphic></graphic> of quasi-constant curvature subject to the condition that the 1-form &#x3B8; and the vector field &#x3B6;, defined by (1.1), are identical with the 1-form &#x3B8; and the vector field &#x3B6; of the indefinite trans-Sasakian structure { J, &#x3B8;, &#x3B6; } of <graphic></graphic>.

On Co-screen Conformality of 1-lightlike Submanifolds in a Lorentzian Manifold

In this paper, the co-screen conformal 1-lightlike submanifolds of a Lorentzian manifoldare introduced as a generalization of co-screen locally half-lightlike submanifolds in(Wang, Wang {\&amp;amp;} Liu, 2013; Wang {\&amp;amp;} Liu, 2013) and two examples are given whichone is co-screen locally conformal andthe other is not. Some results are obtained on these submanifolds whichthe co-screen distribution is conformal Killing on the ambient manifold.The induced Ricci tensor of co-screen conformal 1-lightlike submanifolds isinvestigated.

NON-EXISTENCE OF LIGHTLIKE SUBMANIFOLDS OF INDEFINITE TRANS-SASAKIAN MANIFOLDS WITH NON-METRIC 𝜃-CONNECTIONS

We study two types of 1-lightlike submanifolds, so-called lightlike hypersurface and half lightlike submanifold, of an indefinite trans-Sasakian manifold <TEX>$\bar{M}$</TEX> admitting non-metric <TEX>${\theta}$</TEX>-connection. We prove that there exist no such two types of 1-lightlike submanifolds of an indefinite trans-Sasakian manifold <TEX>$\bar{M}$</TEX> admitting non-metric <TEX>${\theta}$</TEX>-connections.

LIGHTLIKE SUBMANIFOLDS OF A SEMI-RIEMANNIAN MANIFOLD WITH A SEMI-SYMMETRIC NON-METRIC CONNECTION

Abstract. We study the geometry of r-lightlike submanifolds M of asemi-Riemannian manifold M with a semi-symmetric non-metric connec-tion subject to the conditions; (a) the screen distribution of M is to-tally geodesic in M, and (b) at least one among the r-th lightlike secondfundamental forms is parallel with respect to the induced connection ofM. The main result is a classi cation theorem for irrotational r-lightlikesubmanifold of a semi-Riemannian manifold of index r admitting a semi-symmetric non-metric connection. 1. IntroductionThe geometry of lightlike submanifolds is used in mathematical physics, inparticular, in general relativity since lightlike submanifolds produce models ofdi erent types of horizons (event horizons, Cauchy’s horizons, Kruskal’s hori-zons). The universe can be represented as a four dimensional Lorentz subman-ifold (spacetime) embedded in an (n+ 4)-dimensional semi-Riemannian mani-fold. Lightlike hypersurfaces are also studied in the theory of electromagnetism[1]. Thus, large number of applications but limited information available, moti-vated us to do research on this subject matter. Duggal-Bejancu [1] and Kupeli[2] developed the general theory of degenerate (lightlike) submanifolds. Theyconstructed a transversal vector bundle of lightlike submanifold and investi-gated various properties of these manifolds. Duggal-Jin [3] studied totallyumbilical lightlike submanifold of a semi-Riemannian manifold. Ageshe andChae [4] introduced the notion of a semi-symmetric non-metric connection ona Riemannian manifold. Ya˘sar, C˘oken and Yucesan [5] and Jin [6] studied light-like hypersurfaces in semi-Riemannian manifolds admitting a semi-symmetricnon-metric connections. The geometry of half lightlike submanifolds of a semi-Riemannian manifold with semi-symmetric non-metric connection was studied

A semi-Riemannian manifold of quasi-constant curvature with half lightlike submanifolds

A semi-Riemannian manifold of quasi-constant curvature with half lightlike submanifolds

Half lightlike submanifolds of an indefinite generalized Sasakian space form with a quarter-symmetric metric connection

We study the geometry of half lightlike submanifolds of an indenite generalized Sasakian space form M(f1;f2;f3) with a quarter-symmetric metric connection. Our main result is several characterization theorems for such a half lightlike submanifold of M(f1;f2;f3) endowed with an indenite trans-Sasakian structure of type (

A characterization of half lightlike submanifolds of indefinite generalized Sasakian space forms

A characterization of half lightlike submanifolds of indefinite generalized Sasakian space forms