Indefinite Sasakian Manifold Research Articles

Integrability of Distributions in GCR-lightlike Submanifolds of Indefinite Sasakian Manifolds

In this paper, we study GCR-lightlike submanifolds of indefinite Sasakian manifold. We give some necessary and sufficient conditions on integrability of various distributions of GCR-lightlike submanifold of an indefinite Sasakian manifold. We also find the conditions for each leaf of holomorphic distribution and radical distribution is totally geodesic.

Screen Slant Lightlike Submanifolds of Indefinite Sasakian Manifolds

In this paper, we introduce screen slant lightlike submanifold of an indefinite Sasakian manifold and give examples. We prove a characterization theorem for the existence of screen slant lightlike submanifolds. We also obtain integrability conditions of both screen and radical distributions, prove characterization theorems on the existence of minimal screen slant lightlike submanifolds and give an example of proper minimal screen slant lightlike submanifolds of .

SLANT LIGHTLIKE SUBMANIFOLDS OF AN INDEFINITE SASAKIAN MANIFOLD

In this paper, we introduce the notion of a slant lightlike submanifold of an indefinite Sasakian manifold. We provide a non-trivial example and obtain necessary and sufficient conditions for the existence of a slant lightlike submanifold. Also, we prove some characterization theorems.

On indefinite η-Einstein Sasakian manifold

This present paper is to study on indefinite η-Einstein Sasakian manifold which is introduced with an example. Here some properties of indefinite η-Einstein Sasakian manifold have been studied.

Generalized Transversal Lightlike Submanifolds of Indefinite Sasakian Manifolds

We introduce and study generalized transversal lightlike submanifold of indefinite Sasakian manifolds which includes radical and transversal lightlike submanifolds of indefinite Sasakian manifolds as its trivial subcases. A characteristic theorem and a classification theorem of generalized transversal lightlike submanifolds are obtained.

Slant lightlike submanifolds of indefinite Sasakian manifolds

In this paper, we define and study both slant lightlike submanifolds and screen slant lightlike submanifolds of an indefinite Sasakian manifold. We provide non-trivial examples and obtain necessary and sufficient conditions for the existence of a slant lightlike submanifold.

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

Geodesic Lightlike Submanifolds of Indefinite Sasakian Manifolds

In this paper, we study geodesic contact CR-lightlike submanifolds and geodesic screen CR-lightlike (SCR) submanifolds of indefinite Sasakian manifolds. Some necessary and sufficient conditions for totally geodesic, mixed geodesic, -geodesic and -geodesic contact CR-lightlike submanifolds and SCR submanifolds are obtained.

Constancy of ϕ¯‐Holomorphic Sectional Curvature for an Indefinite Generalized g · f · f‐Space Form

Bonome et al., 1997, provided an algebraic characterization for an indefinite Sasakian manifold to reduce to a space of constant ϕ‐holomorphic sectional curvature. In this present paper, we generalize the same characterization for indefinite g · f · f‐space forms.

GCR‐Lightlike Product of Indefinite Sasakian Manifolds

We study mixed geodesic GCR‐lightlike submanifolds of indefinite Sasakian manifolds and obtain some necessary and sufficient conditions for a GCR‐lightlike submanifold to be a GCR‐lightlike product.

Geometry of lightlike hypersurfaces of an indefinite Sasakian manifold

In this paper, we study the geometry of lightlike hypersurfaces of an indefinite Sasakian manifold. The main result is to prove three characterization theorems for such a lightlike hypersurface. In addition to these main theorems, we study the geometry of totally geodesic lightlike hypersurfaces of an indefinite Sasakian manifold.

Symmetry properties of lightlike hypersurfaces in indefinite Sasakian manifolds

In this paper, we investigate symmetry properties of lightlike hypersurfaces in indefinite Sasakian manifolds, tangent to the structure vector field. Theorems on locally symmetric, semi-symmetric and Ricci semi-symmetric lightlike hypersurfaces are obtained. We show that, under some conditions, these hypersurfaces are totally geodesic. The non-existence conditions of specific lightlike hypersurfaces are given. We prove, under a certain condition, that in lightlike hypersurfaces of an indefinite Sasakian space form, tangent to the structure vector field, the local symmetry and semi-symmetry notions are equivalent. This equivalence is extended to the Ricci semi-symmetry notion when the lightlike hypersurfaces are considered to be η-totally umbilical.

Transversal lightlike submanifolds of indefinite sasakian manifolds

We study both radical transversal and transversal lightlike submanifolds of indefinite Sasakian manifolds. We give examples, investigate the geometry of distributions and obtain necessary and sufficient conditions for the induced connection on these submanifolds to be metric connection. We also study totally contact umbilical radical transversal and transversal lightlike submanifolds of indefinite Sasakian manifolds and obtain a classification theorem for totally contact umbilical transversal lightlike submanifolds.

Screen Integrable Lightlike Hypersurfaces of Indefinite Sasakian Manifolds

We investigate lightlike hypersurfaces of indefinite Sasakian manifolds, tangent to the structure vector field ξ and whose screen distribution is integrable. We prove some results on parallel vector fields and on a leaf of the integrable distribution \(D_{0} \perp \langle\xi\rangle\) of this class. A theorem on a geometrical configuration of the screen distribution is obtained. We show that any totally contact umbilical leaf of a screen integrable distribution of a lightlike hypersurface is an extrinsic sphere.

Totally contact umbilical lightlike hypersurfaces of indefinite Sasakian manifolds

This paper investigates totally contact umbilical lightlike hypersurfaces which are tangent to the structure vector field. Theorems on Killing distributions, geodesibility of lightlike hypersurfaces are obtained. The geometrical configuration of such lightlike hypersurfaces and its screen distributions are established. We prove the non-existence of totally contact umbilical lightlike hypersurfaces and lightlike hypersurfaces with totally contact umbilical screen distributions in indefinite Sasakian space forms under some conditions. Some characterizations of totally contact geodesic lightlike hypersurfaces and screen distributions are also given.

Generalized Cauchy-Riemann lightlike submanifolds of indefinite Sasakian manifolds

We study a class of submanifolds, called Generalized Cauchy-Riemann (GCR) lightlike submanifolds of indefinite Sasakian manifolds as an umbrella of invariant, screen real, contact CR lightlike subcases [8] and real hypersurfaces [9]. We prove existence and non-existence theorems and a characterization theorem on minimal GCR-lightlike submanifolds.

On weakly Ricci symmetric lightlike hypersurfaces of indefinite Sasakian manifolds

This paper deals with weakly Ricci-symmetric lightlike hypersurfaces of indefinite Sasakian manifolds, tangent to the structure vector field. We prove that, in a weakly Ricci symmetric lightlike η-Einstein (or Einstein) hypersurface of an indefinite Sasakian manifold, the associated 1-forms α and β satisfy α+β=0 (Theorem 4). Also, we show that there exist no weakly Ricci symmetric screen locally (or globally) conformal lightlike hypersurfaces of indefinite Sasakian manifolds with cyclic parallel Ricci tensor if α+β+γ is not everywhere zero (Theorem 5). A particular case of weakly Ricci symmetric condition is studied and we prove that a special weakly Ricci symmetric screen locally (or globally) conformal lightlike hypersurface cannot be η-Einstein (or Einstein) and under certain condition, it cannot be (D⊥〈 ξ 〉,D')-mixed-totally geodesic (Theorem 7).

Lightlike Submanifolds of Indefinite Sasakian Manifolds

We first prove some results on invariant lightlike submanifolds of indefinite Sasakian manifolds. Then, we introduce a general notion of contact Cauchy-Riemann (CR) lightlike submanifolds and study the geometry of leaves of their distributions. We also study a class, namely, contact screen Cauchy-Riemann (SCR) lightlike submanifolds which include invariant and screen real subcases. Finally, we prove characterization theorems on the existence of contact SCR, screen real, invariant, and contact CR minimal lightlike submanifolds.