Half Lightlike Submanifolds Research Articles

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

In this paper, we study the geometry of half lightlike submanifolds M of a semi-Riemannian manifold <TEX>$\tilde{M}$</TEX> with a semi-symmetric non-metric connection subject to the conditions; (1) the characteristic vector field of <TEX>$\tilde{M}$</TEX> is tangent to M, the screen distribution on M is totally umbilical in M and the co-screen distribution on M is conformal Killing, or (2) the screen distribution is integrable and the local lightlike second fundamental form of M is parallel.

THE CURVATURE OF HALF LIGHTLIKE SUBMANIFOLDS OF A SEMI-RIEMANNIAN MANIFOLD OF QUASI-CONSTANT CURVATURE

We study half lightlike submanifolds M of semi-Riemannian manifolds <TEX>$\widetilde{M}$</TEX> of quasi-constant curvatures. The main result is a characterization theorem for screen homothetic Einstein half lightlike submanifolds of a Lorentzian manifold of quasi-constant curvature subject to the conditions; (1) the curvature vector field of <TEX>$\widetilde{M}$</TEX> is tangent to M, and (2) the co-screen distribution is a conformal Killing one.

EINSTEIN HALF LIGHTLIKE SUBMANIFOLDS WITH SPECIAL CONFORMALITIES

In this paper, we study the geometry of Einstein half lightlike submanifolds M of a semi-Riemannian space form <TEX>$\bar{M}(c)$</TEX> subject to the conditions: (a) M is screen conformal, and (b) the coscreen distribution of M is a conformal Killing one. The main result is a classification theorem for screen conformal Einstein half lightlike submanifolds of a Lorentzian space form with a conformal Killing coscreen distribution.

LOCALLY SYMMETRIC HALF LIGHTLIKE SUBMANIFOLDS IN AN INDEFINITE KENMOTSU MANIFOLD

In this paper, we study locally symmetric half lightlike submanifolds M of an indefinite Kenmotsu manifold <TEX>$\bar{M}$</TEX> subject to the conditions: (1) The transversal vector bundle <TEX>$tr(TM)$</TEX> is parallel with respect to the connection <TEX>$\bar{\nabla}$</TEX> of <TEX>$\bar{M}$</TEX> and (2) M is irrotational.

HALF LIGHTLIKE SUBMANIFOLDS IN INDEFINITE $S$-MANIFOLDS

In an indefinite metric $g.f.f$-manifold, we study half lightlike submanifolds $M$ tangent to the characteristic vector fields. We discuss the existence of totally umbilical half lightlike submanifolds of an indefinite $\cal{S}$-space form.

Special Half Lightlike Submanifolds of an Indefinite Cosymplectic Manifold

We study the geometry of half lightlike submanifolds 𝑀 of an indefinite cosymplectic manifold 𝑀. First, we construct two types of half lightlike submanifolds according to the form of the structure vector field of 𝑀, named by tangential and ascreen half lightlike submanifolds. Next, we characterize the lightlike geometries of such two types of half lightlike submanifolds.

REAL HALF LIGHTLIKE SUBMANIFOLDS OF AN INDEFINITE KAEHLER MANIFOLD

In this paper, we study the geometry of real half lightlike submanifolds of an indefinite Kaehler manifold <TEX>$\bar{M}$</TEX>. We provide several new results on such a real half lightlike submanifold M by using the F-structure of M induced by the almost complex structure J of <TEX>$\bar{M}$</TEX>.

HALF LIGHTLIKE SUBMANIFOLDS OF AN INDEFINITE SASAKIAN MANIFOLD

We study half lightlike submanifolds of an indefinite Sasakian manifold. The aim of this paper is to prove the following result: If a locally symmetric half lightlike submanifold of an indefinite Sasakian manifold is totally umbilical, then it is of constant positive curvature 1. In addition to this result, we prove three characterization theorems for such a half lightlike submanifold.

TRANSVERSAL HALF LIGHTLIKE SUBMANIFOLDS OF AN INDEFINITE SASAKIAN MANIFOLD

Abstract. In this paper, we study the geometry of half lightlike sub-manifolds of an indefinite Sasakian manifold. There are several differenttypes of half lightlike submanifolds of an indefinite Sasakian manifold ac-cording to the form of its structure vector field. We study two types ofthem here: tangential and ascreen half lightlike submanifolds. 1. IntroductionThe class of codimension 2 lightlike submanifolds of semi-Riemannian man-ifolds is compose of two classes by virtue of the rank of its radical distribution,which are called half lightlike submanifold or coisotropic submanifold [5]. Halflightlike submanifold is a particular case of r-lightlike submanifold [4] suchthat r = 1 and its geometry is more general form than that of coisotrophicsubmanifolds or lightlike hypersurfaces. Much of the works on half lightlikesubmanifolds will be immediately generalized in a formal way to arbitrary r-lightlike submanifolds. Recently many authors have studied the geometry oflightlike submanifolds of indefinite Sasakian manifolds [7, 8, 9, 12].In this paper, we study two types of half lightlike submanifolds of an indefi-nite Sasakian manifold, named by tangential and ascreen half lightlike subman-ifolds. In Section 3, we prove three characterization theorems for tangentialhalf lightlike submanifolds: (1) There exists no screen conformal tangentialhalf lightlike submanifold of an indefinite Sasakian manifold. (2) There ex-ists no tangential half lightlike submanifold of an indefinite Sasakian manifoldsuch that its screen distribution is totally umbilical. (3) There exists no to-tally umbilical tangential half lightlike submanifold of an indefinite Sasakianmanifold.In Section 4, we prove three characterization theorems for ascreen half light-like submanifolds: (1) There exists no screen conformal ascreen half lightlikesubmanifold of an indefinite Sasakian manifold. (2) There exists no ascreen half

GEOMETRY OF SCREEN CONFORMAL REAL HALF LIGHTLIKE SUBMANIFOLDS

In this paper, we study the geometry of real half lightlike submanifolds of an indefinite Kaehler manifold. The main result is a characterization theorem for screen conformal real half lightlike submanifolds of an indefinite complex space form.

A CHARACTERIZATION OF SCREEN CONFORMAL HALF LIGHTLIKE SUBMANIFOLDS

We study the geometry of screen conformal half lightlike submanifolds of a semi-Riemannian manifod. The main result is a classification theorem for screen conformal half lightlike submanifolds of a semi-Riemannian space form with a Killing co-screen distribution.

EINSTEIN HALF LIGHTLIKE SUBMANIFOLDS WITH A KILLING CO-SCREEN DISTRIBUTION

In this paper we study the geometry of codimension 2 screen conformal Einstein half lightiike submanifolds M of a semi-Riemannian manifold <TEX>$(\={M}(c),\={g})$</TEX> of constant curvature c, with a Killing co-screen distribution on <TEX>$\={M}$</TEX>. The main result is a classification theorem for screen homothetic Einstein half lightlike submanifold of Lorentzian space forms.