Indefinite Sasakian Manifold Research Articles

SCREEN PSEUDO-SLANT LIGHTLIKE SUBMERSIONS FROM INDEFINITE SASAKIAN MANIFOLDS ONTO LIGHTLIKE MANIFOLDS

As a generalization of screen slant lightlike submersions, we introduce the notion of screen pseudo-slant lightlike submersions from indefinite Sasakian manifolds onto lightlike manifolds. We give examples and prove a characterization theorem for the existence of such lightlike submersions. We also obtain integrability conditions of distributions involved in the definition of this class of lightlike submersions. Further, we find necessary and sufficient conditions for foliations determined by these distributions to be totally geodesic.

Radical transversal screen pseudo-slant lightlike submersions from indefinite Sasakian manifolds onto lightlike manifolds

As a generalization of transversal and radical transversal screen slant lightlike submersions, we introduce the notion of radical transversal screen pseudo-slant lightlike submersions from indefinite Sasakian manifolds onto lightlike manifolds with examples. We obtain an existence theorem for such lightlike submersions and study the geometry of distributions involved in the definition.

Contact screen transversal Cauchy-Riemann lightlike submanifolds of indefinite Sasakian manifolds

We study contact screen transversal Cauchy-Riemann (STCR)-lightlike submanifolds of indefinite Sasakian manifolds. We prove existence and non-existence theorems and find the integrability conditions of integrability of various distributions. We derive some characterization theorems for a contact STCR-lightlike submanifold to be a STCR-lightlike product. Moreover, we find results for minimal contact STCR-lightlike submanifolds of indefinite Sasakian manifolds. We also give examples.

On contact screen conformal null submanifolds

First, we prove that indefinite Sasakian manifolds do not admit any screen conformal $r$-null submanifolds, tangent to the structure vector field. We, therefore, define a special class of null submanifolds, called; {\it contact screen conformal} $r$-null submanifold of indefinite Sasakian manifolds. Several characterization results, on the above class of null submanifolds, are proved. In particular, we prove that such null submanifolds exist in indefinite Sasakian space forms of constant holomorphic sectional curvatures of $-3$.

On certain principal directions in lightlike hypersurfaces of an indefinite Sasakian manifold

On certain principal directions in lightlike hypersurfaces of an indefinite Sasakian manifold

On recurrent Light like Hypersurfaces of Indefinite Sasakian Manifold

The object of present paper is to study the properties of recurrent lightlike hypersurfaces of indefinite Sasakian manifold with (l, m) –type connection.

Some remarks on invariant lightlike submanifolds of indefinite Sasakian manifold

PurposeThe author considers an invariant lightlike submanifold M, whose transversal bundle tr(TM) is flat, in an indefinite Sasakian manifold M¯(c) of constant φ¯-sectional curvature c. Under some geometric conditions, the author demonstrates that c=1, that is, M¯ is a space of constant curvature 1. Moreover, M and any leaf M′ of its screen distribution S(TM) are, also, spaces of constant curvature 1.Design/methodology/approachThe author has employed the techniques developed by K. L. Duggal and A. Bejancu of reference number 7.FindingsThe author has discovered that any totally umbilic invariant ligtlike submanifold, whose transversal bundle is flat, in an indefinite Sasakian space form is, in fact, a space of constant curvature 1 (see Theorem 4.4).Originality/valueTo the best of the author’s findings, at the time of submission of this paper, the results reported are new and interesting as far as lightlike geometry is concerned.

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.

Radical transversal SCR-lightlike submanifolds of indefinite Sasakian manifolds

In this paper, we introduce the notion of radical transversal screen Cauchy-Riemann (SCR)- lightlike submanifolds of indefinite Sasakian manifolds giving characterization theorem with some nontrivial examples of such submanifolds. Integrability conditions of distributions D1, D2, D and D? on radical transversal SCR-lightlike submanifolds of an indefinite Sasakian manifold have been obtained. Further, we obtain necessary and sufficient conditions for foliations determined by above distributions to be totally geodesic.

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.

Riemannian Curvature of a Sliced Contact Metric Manifold

Contact geometry become a more important issue in the mathematical world with the works which had done in the 19th century. Many mathematicians have made studies on contact manifolds, almost contact manifolds, almost contact metric manifolds and contact metric manifolds. Many different studies have been done and papers have been published on Sasaki manifolds, Kähler manifolds, the other manifold types and submanifolds of them. In our previous studies we get the characterization of indefinite Sasakian manifolds. In order to get the characterization of indefinite Sasakian manifolds, firstly we defined sliced contact metric manifolds and then we examined the features of them. As a result we obtain a sliced almost contact metric manifold which is a wider class of almost contact metric manifolds. Thus, we constructed a sliced which is a contact metric manifold on an almost contact metric manifold where the manifold is not a contact metric manifold. Sliced almost contact metric manifolds generalized the almost contact metric manifolds. Then, we study on the sliced Sasakian manifolds and the submanifolds of them. Moreover we analyzed some important properties of the manifold theory on sliced almost contact metric manifolds.In this paper we calculated the -sectional curvature and the Riemannian curvature tensor of the sliced almost contact metric manifolds. Hence we think that all these studies will accelerate the studies on the contact manifolds and their submanifolds.

Some characterization theorems on holomorphic sectional curvature of GCR-lightlike submanifolds

We obtain the expressions for sectional curvature, holomorphic sectional curvature and holomorphic bisectional curvature of a GCR-lightlike submanifold of an indefinite Sasakian manifold and obtain some characterization theorems on holomorphic sectional and holomorphic bisectional curvature.

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.

LIGHTLIKE SUBMANIFOLDS OF AN INDEFINITE SASAKIAN MANIFOLD WITH A NON-METRIC θ-CONNECTION

In this paper, we study two types of 1-lightlike submanifolds, named by lightlike hypersurface and half lightlike submanifold, of an indefinite Sasakian manifold admitting non-metric <TEX>${\theta}$</TEX>-connections. We prove that there exist no such two types of 1-lightlike submanifolds of an indefinite Sasakian manifold.

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

SPECIAL HALF LIGHTLIKE SUBMANIFOLDS OF AN INDEFINITE SASAKIAN MANIFOLD

In this paper, we study the geometry of half lightlike submanifolds of an indefinite Sasakian manifold. There are several different types of half lightlike submanifolds of an indefinite Sasakian manifold according to the form of its structure vector field. We study two types of them here: tangential and ascreen half lightlike submanifolds.

Submanifolds of some indefinite contact and paracontact manifolds

The purpose of the present paper is to study some types of submanifolds of indefinite contact and paracontact manifolds and a few properties of contact CR-submanifolds of an indefinite Sasakian manifold, indefinite Kenmotsu manifold, indefinite trans-Sasakian manifold and ε-paracontact Sasakian manifold.

Characterization of GCR-lightlike warped product of indefinite Sasakian manifolds

In this paper we prove that there do not exist warped product GCR-lightlike submanifolds in the form M=N⊥×λNT such that N⊥ is an anti-invariant submanifold tangent to V and NT an invariant submanifold of M‾, other than GCR-lightlike product in an indefinite Sasakian manifold. We also obtain characterization theorems for a GCR-lightlike submanifold to be locally a GCR-lightlike warped product.