Submanifolds Of Indefinite Sasakian Manifolds Research Articles

η-Ricci-Yamabe solitons on submanifolds of some indefinite almost contact manifolds

In this paper, we study the η-Ricci-Yamabe soliton on invariant and anti-invariant submanifolds of indefinite Sasakian manifolds, indefinite Kenmotsu manifolds and indefinite trans-Sasakian manifolds concerning Riemannian connection and quarter symmetric metric connection.

Screen Generic Lightlike Submanifolds of Indefinite Sasakian Manifolds

In this paper, we introduce the general notion of screen generic lightlike submanifolds of indefinite Sasakian manifolds. We study screen generic lightlike submnaifolds, contact totally umbilical screen generic lightlike submanifolds, and minimal screen generic lightlike submanifolds of indefinite Sasakian manifolds. Also, we provide some examples of screen generic lightlike submanifold and minimal screen generic lightlike submanifold of an indefinite Sasakian manifold.

Screen Semi-Slant Lightlike Submanifolds of Indefinite Sasakian Manifolds

In this paper, we introduce the notion of screen semi-slant lightlike submanifolds of indefinite Sasakian manifolds giving characterization theorem with some non-trivial examples of such submanifolds. Integrability conditions of distributions D1, D2 and RadTM on screen semi-slant lightlike submanifolds of indefinite Sasakian manifolds have been obtained. Further we obtain necessary and sufficient conditions for foliations determined by above distributions to be totally geodesic. We also study mixed geodesic screen semi-slant lightlike submanifolds of indefinite Sasakian manifolds and obtain a necessary and sufficient condition for induced connection to be metric connection.

Radical transversal screen semi-slant lightlike submanifolds of indefinite Sasakian manifolds

In this paper, we introduce the notion of radical transversal screen semi-slant lightlike submanifolds of indefinite Sasakianmanifolds giving some non-trivial examples and give characterization theorem of such submanifolds. Integrability conditions of distributions D 1, D 2 and RadTM on radical transversal screen semi-slant lightlike submanifolds of indefinite Sasakian manifolds have been obtained. Further we obtain necessary and sufficient conditions for foliations determined by above distributions to be totally geodesic. We also study mixed geodesic radical transversal screen semi-slant lightlike submanifolds of indefinite Sasakian manifolds.

Screen Pseudo-Slant Lightlike Submanifolds of Indefinite Sasakian Manifolds

In this paper, we introduce the notion of screen pseudo-slant lightlike submanifolds of indefinite Sasakian manifolds giving characterization theorem with some non-trivial examples of such submanifolds. Integrability conditions of distributions D1, D2 and RadTM on screen pseudo-slant lightlike submanifolds of indefinite Sasakian manifolds have been obtained. Further, we obtain necessary and sufficient conditions for foliations determined by above distributions to be totally geodesic. We also study mixed geodesic screen pseudo-slant lightlike submanifolds of indefinite Sasakian manifolds.

On Totally Contact Umbilical Contact CR-Lightlike Submanifolds Of Indefinite Sasakian Manifolds

AbstractAfter brief introduction, we prove that a totally contact umbilical CR- lightlike submanifold is totally contact geodesic. We obtain a necessary and sufficient condition for a CR-lightlike submanifold to be an anti-invariant submanifold. Finally, we characterize a contact CR-lightlike submanifold of indefinite Sasakian manifold to be a contact CR-lightlike product

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.

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.

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.

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.

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.

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.

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.