scholarly journals The geometry of contact pseudo-slant submanifolds of a Sasakian manifold

Filomat ◽  
2019 ◽  
Vol 33 (17) ◽  
pp. 5551-5559
Author(s):  
Ümit Yıldırım
Keyword(s):  
Tensor Field ◽  
Sufficient Conditions ◽  
Sasakian Manifold ◽  
Necessary And Sufficient Conditions ◽  
Slant Submanifold ◽  
Slant Submanifolds ◽  
Necessary And Sufficient

In this paper, we study the geometry of the contact pseudo-slant submanifolds of a Sasakian manifold. We verify some properties of the components of the tensor field acting on that kind of submanifold and find out the necessary and sufficient conditions for them to be parallel. Also, necessary and sufficient conditions are given for a submanifold to be a pseudo-slant submanifold, contact pseudo-slant product, D?, D? and mixed-geodesic in Sasakian manifold.

scholarly journals On warped product semi-slant submanifolds of nearly Trans-Sasakian manifolds

Filomat ◽  
2018 ◽  
Vol 32 (17) ◽  
pp. 5845-5856
Author(s):  
Akram Ali ◽  
Ali Alkhaldi ◽  
Rifaqat Ali
Keyword(s):  
Warped Product ◽  
Sufficient Conditions ◽  
Characterization Theorem ◽  
Sasakian Manifold ◽  
Necessary And Sufficient Conditions ◽  
Sasakian Manifolds ◽  
Slant Submanifold ◽  
Slant Submanifolds ◽  
Necessary And Sufficient

In this paper, we study warped product semi-slant submanifold of type M = NT xf N? with slant fiber, isometrically immersed in a nearly Trans-Sasakian manifold by finding necessary and sufficient conditions in terms of Weingarten map. A characterization theorem is proved as main result.

scholarly journals Some Result on Contact Pseudo-Slant Submanifolds of a Sasakian Manifold

2019 ◽  
Vol 17 ◽  
pp. 414-425
Author(s):  
Suleyman Dirik
Keyword(s):  
Sufficient Conditions ◽  
Sasakian Manifold ◽  
Necessary And Sufficient Conditions ◽  
Slant Submanifold ◽  
Slant Submanifolds ◽  
Integrability Conditions ◽  
Definition Of ◽  
Necessary And Sufficient

In this paper, we study the geometry of the contact pseudo-slant submanifolds of a Sasakian manifold. We derive the integrability conditions of distributions in the definition of a contact pseudo-slant submanifold. The notions contact pseudo-slant product is defined, and the necessary and sufficient conditions for a submanifold to contact pseudo-slant product is given. Also, a non-trivial example is used to demonstrate that the method presented in this paper is effective.

scholarly journals Para-CR structures on almost paracontact metric manifolds

2014 ◽  
Vol 20 (2) ◽  
Author(s):  
Joanna Wełyczko
Keyword(s):  
Sectional Curvature ◽  
Sufficient Conditions ◽  
Sasakian Manifold ◽  
Necessary And Sufficient Conditions ◽  
Constant Sectional Curvature ◽  
Conformally Flat ◽  
Cr Manifolds ◽  
Cosymplectic Manifolds ◽  
Cr Structures ◽  
Necessary And Sufficient

AbstractAlmost paracontact metric manifolds are the famous examples of almost para-CR manifolds. We find necessary and sufficient conditions for such manifolds to be para-CR. Next we examine these conditions in certain subclasses of almost paracontact metric manifolds. Especially, it is shown that normal almost paracontact metric manifolds are para-CR. We establish necessary and sufficient conditions for paracontact metric manifolds as well as for almost para-cosymplectic manifolds to be para-CR. We find also basic curvature identities for para-CR paracontact metric manifolds and study their consequences. Among others, we prove that any para-CR paracontact metric manifold of constant sectional curvature and of dimension greater than 3 must be para-Sasakian and its curvature equal to -1. The last assertion does not hold in dimension 3. We show that a conformally flat para-Sasakian manifold is of constant sectional curvature equal to -1. New classes of examples of para-CR manifolds are established.

TENSORIAL CURVATURE AND D-DIFFERENTIATION PART II: "PRINCIPAL" KIND AND EINSTEIN–MAXWELL THEORY

2007 ◽  
Vol 04 (05) ◽  
pp. 847-860 ◽  
Author(s):  
D. J. HURLEY ◽  
M. A. VANDYCK
Keyword(s):  
Scalar Curvature ◽  
Tensor Field ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Curvature Operator ◽  
Maxwell Theory ◽  
Covariant Differentiation ◽  
Necessary And Sufficient

The class of "commutative" D-operators, which was introduced in the first part of this paper, is generalized to obtain the "principal" class. It is established that principal D-operators are expressible in terms of covariant differentiation and a tensor field. Necessary and sufficient conditions are determined for the curvature operator to be tensorial, and for the scalar curvature to exist. As an application, the Einstein–Maxwell theory is recast in a new geometrical framework.

On η-Einstein Trans-Sasakian Manifolds

2011 ◽  
Vol 57 (2) ◽  
pp. 417-440
Author(s):  
Falleh Al-Solamy ◽  
Jeong-Sik Kim ◽  
Mukut Tripathi
Keyword(s):  
Vector Field ◽  
Sufficient Conditions ◽  
Sasakian Manifold ◽  
Necessary And Sufficient Conditions ◽  
Sasakian Manifolds ◽  
Contact Metric Manifold ◽  
Almost Contact Metric Manifold ◽  
3 Dimensional ◽  
Almost Contact Metric ◽  
Necessary And Sufficient

On η-Einstein Trans-Sasakian ManifoldsA systematic study of η-Einstein trans-Sasakian manifold is performed. We find eight necessary and sufficient conditions for the structure vector field ζ of a trans-Sasakian manifold to be an eigenvector field of the Ricci operator. We show that for a 3-dimensional almost contact metric manifold (M,φ, ζ, η, g), the conditions of being normal, trans-K-contact, trans-Sasakian are all equivalent to ∇ζ ∘ φ = φ ∘ ∇ζ. In particular, the conditions of being quasi-Sasakian, normal with 0 = 2β = divζ, trans-K-contact of type (α, 0), trans-Sasakian of type (α, 0), andC6-class are all equivalent to ∇ ζ = -αφ, where 2α = Trace(φ∇ζ). In last, we give fifteen necessary and sufficient conditions for a 3-dimensional trans-Sasakian manifold to be η-Einstein.

On non-invariant hypersurfaces of a nearly hyperbolic Sasakian manifold

2017 ◽  
Vol 28 (08) ◽  
pp. 1750064
Author(s):  
Mobin Ahmad ◽  
Shadab Ahmad Khan ◽  
Toukeer Khan
Keyword(s):  
Fundamental Form ◽  
Sufficient Conditions ◽  
Sasakian Manifold ◽  
Second Fundamental Form ◽  
Text Structure ◽  
Necessary And Sufficient Conditions ◽  
Totally Geodesic ◽  
Totally Umbilical ◽  
The Second Fundamental Form ◽  
Necessary And Sufficient

We consider a nearly hyperbolic Sasakian manifold equipped with [Formula: see text]-structure and study non-invariant hypersurface of a nearly hyperbolic Sasakian manifold equipped with [Formula: see text]-structure. We obtain some properties of nearly hyperbolic Sasakian manifold equipped with [Formula: see text]-structure. Further, we find the necessary and sufficient conditions for totally umbilical non-invariant hypersurface with [Formula: see text]-structure of nearly hyperbolic Sasakian manifold to be totally geodesic. We also calculate the second fundamental form of a non-invariant hypersurface of a nearly hyperbolic Sasakian manifold with [Formula: see text]-structure under the condition when f is parallel.

scholarly journals Some Conditions on Trans-Sasakian Manifolds to Be Homothetic to Sasakian Manifolds

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1887
Author(s):  
Sharief Deshmukh ◽  
Amira Ishan ◽  
Olga Belova ◽  
Suha B. Al-Shaikh
Keyword(s):  
Sufficient Conditions ◽  
Sasakian Manifold ◽  
Necessary And Sufficient Conditions ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Sasakian Manifolds ◽  
3 Dimensional ◽  
Necessary And Sufficient ◽  
Simply Connected

In this paper, we study 3-dimensional compact and connected trans-Sasakian manifolds and find necessary and sufficient conditions under which these manifolds are homothetic to Sasakian manifolds. First, four results in this paper deal with finding necessary and sufficient conditions on a compact and connected trans-Sasakian manifold to be homothetic to a compact and connected Sasakian manifold, and the fifth result deals with finding necessary and sufficient condition on a connected trans-Sasakian manifold to be homothetic to a connected Sasakian manifold. Finally, we find necessary and sufficient conditions on a compact and simply connected trans-Sasakian manifold to be homothetic to a compact and simply connected Einstein Sasakian manifold.

scholarly journals Contact co-isotropic CR submanifolds of a pseudo-Sasakian manifold

1984 ◽  
Vol 7 (2) ◽  
pp. 339-350 ◽  
Author(s):  
Vladislav V. Goldberg ◽  
Radu Rosca
Keyword(s):  
Vertical Distribution ◽  
Sufficient Conditions ◽  
Sasakian Manifold ◽  
Necessary And Sufficient Conditions ◽  
Totally Geodesic ◽  
Isotropic Submanifold ◽  
Cr Submanifold ◽  
Necessary And Sufficient ◽  
Cr Submanifolds

It is proved that any co-isotropic submanifoldMof a pseudo-Sasakian manifoldM˜(U,ξ,η˜,g˜)is a CR submanifold (such submanfolds are called CICR submanifolds) with involutive vertical distributionν1. The leavesM1ofD1are isotropic andMisν1-totally geodesic. IfMis foliate, thenMis almost minimal. IfMis RicciD1-exterior recurrent, thenMreceives two contact Lagrangian foliations. The necessary and sufficient conditions forMto be totally minimal is thatMbe contactD1-exterior recurrent.

scholarly journals Warped product semi-slant submanifolds in locally conformal Kaehler manifolds

2017 ◽  
Vol 10 (2) ◽  
Author(s):  
Koji Matsumoto
Keyword(s):  
Warped Product ◽  
Sufficient Conditions ◽  
Hermitian Manifold ◽  
Kaehler Manifold ◽  
Slant Submanifold ◽  
Kaehler Manifolds ◽  
Slant Submanifolds ◽  
Necessary And Sufficient ◽  
Locally Conformal ◽  
Nearly Kaehler Manifold

In 1994, in [13], N. Papaghiuc introduced the notion of semi-slant submanifold in a Hermitian manifold which is a generalization of CR- and slant-submanifolds. In particular, he considered this submanifold in Kaehlerian manifolds, [13]. Then, in 2007, V. A. Khan and M. A. Khan considered this submanifold in a nearly Kaehler manifold and obtained interesting results, [11]. Recently, we considered semi-slant submanifolds in a locally conformal Kaehler manifold and gave a necessary and sufficient conditions for two distributions (holomorphic and slant) to be integrable. Moreover, we considered these submanifolds in a locally conformal Kaehler space form, [4]. In this paper, we define 2-kind warped product semi-slant submanifolds in a locally conformal Kaehler manifold and consider some properties of these submanifolds.

scholarly journals Slant lightlike submanifolds of indefinite Sasakian manifolds

Filomat ◽  
2012 ◽  
Vol 26 (2) ◽  
pp. 277-287 ◽  
Author(s):  
Bayram Sahin ◽  
Cumali Yıldırım
Keyword(s):  
Sufficient Conditions ◽  
Sasakian Manifold ◽  
Necessary And Sufficient Conditions ◽  
Sasakian Manifolds ◽  
Necessary And Sufficient ◽  
Lightlike Submanifolds ◽  
Lightlike Submanifold

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.

Sign in / Sign up

Export Citation Format

Share Document