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 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 Radical transversal SCR-lightlike submanifolds of indefinite Sasakian manifolds

Filomat ◽  
2021 ◽  
Vol 35 (8) ◽  
pp. 2585-2594
Author(s):  
S.S. Shukla ◽  
Akhilesh Yadav
Keyword(s):  
Sufficient Conditions ◽  
Characterization Theorem ◽  
Sasakian Manifold ◽  
Necessary And Sufficient Conditions ◽  
Sasakian Manifolds ◽  
Totally Geodesic ◽  
Integrability Conditions ◽  
Cauchy Riemann ◽  
Necessary And Sufficient ◽  
Lightlike Submanifolds

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.

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.

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 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.

ON PROJECTIVELY RELATED WARPED PRODUCT FINSLER MANIFOLDS

2011 ◽  
Vol 08 (05) ◽  
pp. 953-967 ◽  
Author(s):  
M. M. REZAII ◽  
Y. ALIPOUR-FAKHRI
Keyword(s):  
Warped Product ◽  
Sufficient Conditions ◽  
Linear Connection ◽  
Necessary And Sufficient Conditions ◽  
Finsler Manifolds ◽  
Non Linear ◽  
Necessary And Sufficient

Let 𝔽1 = (M1,F1) and 𝔽2 = (M2,F2) be two Finsler manifolds and let M = M1 × M2 and S is a spray in M. Also 𝔽 = (M1 × f M2, F) is a warped product Finsler manifolds, such that the function f : M1 → ℝ+ is not constant. In this paper, we define a non-linear connection on warped product 𝔽, and finally, we have presented some necessary and sufficient conditions under which the spray manifold (M1 × M2, S) is projectively equivalent to the warped product Finsler manifolds (M1 × f M2, F).

scholarly journals Warped Product Submanifolds of LP-Sasakian Manifolds

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
S. K. Hui ◽  
S. Uddin ◽  
C. Özel ◽  
A. A. Mustafa
Keyword(s):  
Warped Product ◽  
Sasakian Manifold ◽  
Sasakian Manifolds ◽  
Slant Submanifolds

We study of warped product submanifolds, especially warped product hemi-slant submanifolds of LP-Sasakian manifolds. We obtain the results on the nonexistance or existence of warped product hemi-slant submanifolds and give some examples of LP-Sasakian manifolds. The existence of warped product hemi-slant submanifolds of an LP-Sasakian manifold is also ensured by an interesting example.

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.

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