scholarly journals Warped product pointwise bi-slant submanifolds of trans-Sasakian manifold

2020 ◽  
Vol 29 (2) ◽  
pp. 171-182
Author(s):  
Pahan Sampa
Keyword(s):  
Warped Product ◽  
Sasakian Manifold ◽  
Ricci Soliton ◽  
Einstein Manifolds ◽  
Slant Submanifold ◽  
Contact Metric Manifold ◽  
Almost Contact Metric Manifold ◽  
Slant Submanifolds ◽  
Almost Contact Metric ◽  
In Trans

The purpose of this paper is to study pointwise bi-slant submanifolds of trans-Sasakian manifold. Firstly, we obtain a non-trivial example of a pointwise bi-slant submanifolds of an almost contact metric manifold. Next we provide some fundamental results, including a characterization for warped product pointwise bi-slant submanifolds in trans-Sasakian manifold. Then we establish that there does not exist warped product pointwise bi-slant submanifold of trans-Sasakian manifold \tilde{M} under some certain considerations. Next, we consider that M is a proper pointwise bi-slant submanifold of a trans-Sasakian manifold \tilde{M} with pointwise slant distrbutions \mathcal{D}_1\oplus<\xi> and \mathcal{D}_2, then using Hiepko’s Theorem, M becomes a locally warped product submanifold of the form M_1\times_fM_2, where M_1 and M_2 are pointwise slant submanifolds with the slant angles \theta_1 and \theta_2 respectively. Later, we show that pointwise bi-slant submanifolds of trans-Sasakian manifold become Einstein manifolds admitting Ricci soliton and gradient Ricci soliton under some certain conditions..

Almost bi-slant submanifolds of an almost contact metric manifold

2020 ◽  
Vol 112 (1) ◽  
Author(s):  
Selcen Yüksel Perktaş ◽  
Adara M. Blaga ◽  
Erol Kılıç
Keyword(s):  
Contact Metric Manifold ◽  
Almost Contact Metric Manifold ◽  
Slant Submanifolds ◽  
Almost Contact Metric

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 ∇N-EINSTEIN ALMOST CONTACT METRIC MANIFOLDS

2021 ◽  
pp. 5-15
Author(s):  
S.V. Galaev ◽  
Keyword(s):  
Tangent Bundle ◽  
Einstein Manifolds ◽  
Contact Metric Manifold ◽  
Contact Manifolds ◽  
Almost Contact Metric Manifold ◽  
Contact Metric Manifolds ◽  
Metric Connection ◽  
Almost Contact Metric ◽  
Almost Contact Metric Manifolds

On an almost contact metric manifold M, an N-connection ∇N defined by the pair (∇,N), where ∇ is the interior metric connection and N: TМ → TM is an endomorphism of the tangent bundle of the manifold M such that Nξ = 0, 􀁇 􀁇 N (D) ⊂ D , is considered. Special attention is paid to the case of a skew-symmetric N-connection ∇N, which means that the torsion of an N-connection considered as a trivalent covariant tensor is skew-symmetric. Such a connection is uniquely defined and corresponds to the endomorphism N = 2ψ, where the endomorphism ψ is defined by the equality ω( X ,Y ) = g (ψX ,Y ) and is called in this work the second structure endomorphism of an almost contact metric manifold. The notion of a ∇N-Einstein almost contact metric manifold is introduced. For the case N = 2ψ, conditions under which almost contact manifolds are ∇N-Einstein manifolds are found.

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 Skew semi-invariant submanifolds of generalized quasi-Sasakian manifolds

2018 ◽  
Vol 9 (2) ◽  
pp. 188-197 ◽  
Author(s):  
M.D. Siddiqi ◽  
A. Haseeb ◽  
M. Ahmad
Keyword(s):  
Sasakian Manifold ◽  
Equivalence Relations ◽  
Cr Manifold ◽  
Sasakian Manifolds ◽  
Invariant Submanifold ◽  
Contact Metric Manifold ◽  
Almost Contact Metric Manifold ◽  
New Class ◽  
Almost Contact Metric ◽  
Invariant Submanifolds

In the present paper,  we study a new class of submanifolds of a generalized Quasi-Sasakian manifold, called skew semi-invariant submanifold. We obtain integrability conditions of the distributions on a skew semi-invariant submanifold and also find the condition for a skew semi-invariant submanifold  of a generalized Quasi-Sasakian manifold to be mixed totally geodesic. Also it is shown that a  skew semi-invariant submanifold of a generalized Quasi-Sasakian manifold will be anti-invariant if and only if $A_{\xi}=0$; and the submanifold will be skew semi-invariant submanifold if $\nabla w=0$. The equivalence relations for the  skew semi-invariant submanifold of a  generalized Quasi-Sasakian manifold are given. Furthermore, we have proved that a skew semi-invariant $\xi^\perp$-submanifold of a normal almost contact metric manifold and a generalized Quasi-Sasakian manifold with non-trivial invariant distribution is $CR$-manifold. An example of dimension 5 is given to show that a skew semi-invariant $\xi^\perp$ submanifold is a $CR$-structure on the manifold.

scholarly journals SLANT SUBMANIFOLDS IN SASAKIAN MANIFOLDS

2000 ◽  
Vol 42 (1) ◽  
pp. 125-138 ◽  
Author(s):  
J. L. Cabrerizo ◽  
A. Carriazo ◽  
L. M. Fernández ◽  
M. Fernández
Keyword(s):  
Special Class ◽  
Three Dimensional ◽  
Subject Classification ◽  
Sasakian Manifolds ◽  
Contact Metric Manifold ◽  
Almost Contact Metric Manifold ◽  
Slant Submanifolds ◽  
Almost Contact Metric

In this paper, we show new results on slant submanifolds of an almost contact metric manifold. We study and characterize slant submanifolds of K-contact and Sasakian manifolds. We also study the special class of three-dimensional slant submanifolds. We give several examples of slant submanifolds.1991 Mathematics Subject Classification 53C15, 53C40.

Pointwise pseudo-slant submanifolds of a Kenmotsu manifold

Filomat ◽  
2017 ◽  
Vol 31 (18) ◽  
pp. 5833-5853 ◽  
Author(s):  
Viqar Khan ◽  
Mohammad Shuaib
Keyword(s):  
Present Article ◽  
Warped Product ◽  
Shape Operator ◽  
Warped Products ◽  
Canonical Structure ◽  
Slant Submanifold ◽  
Kenmotsu Manifold ◽  
Slant Submanifolds ◽  
Kenmotsu Manifolds

In the present article, we have investigated pointwise pseudo-slant submanifolds of Kenmotsu manifolds and have sought conditions under which these submanifolds are warped products. To this end first, it is shown that these submanifolds can not be expressed as non-trivial doubly warped product submanifolds. However, as there exist non-trivial (single) warped product submanifolds of a Kenmotsu manifold, we have worked out characterizations in terms of a canonical structure T and the shape operator under which a pointwise pseudo slant submanifold of a Kenmotsu manifold reduces to a warped product submanifold.

scholarly journals Geometric Mechanics on Warped Product Semi-Slant Submanifold of Generalized Complex Space Forms

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Yanlin Li ◽  
Ali H. Alkhaldi ◽  
Akram Ali
Keyword(s):  
Warped Product ◽  
Complex Space ◽  
Slant Submanifold ◽  
Codazzi Equation ◽  
Space Forms ◽  
Kaehler Manifolds ◽  
Slant Submanifolds ◽  
Generalized Complex ◽  
Complex Space Forms ◽  
Nearly Kaehler Manifold

In this study, we develop a general inequality for warped product semi-slant submanifolds of type M n = N T n 1 × f N ϑ n 2 in a nearly Kaehler manifold and generalized complex space forms using the Gauss equation instead of the Codazzi equation. There are several applications that can be developed from this. It is also described how to classify warped product semi-slant submanifolds that satisfy the equality cases of inequalities (determined using boundary conditions). Several results for connected, compact warped product semi-slant submanifolds of nearly Kaehler manifolds are obtained, and they are derived in the context of the Hamiltonian, Dirichlet energy function, gradient Ricci curvature, and nonzero eigenvalue of the Laplacian of the warping functions.

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.

Lifting semi-invariant submanifolds to distribu­tion of almost contact metric manifolds

2020 ◽  
pp. 39-48
Author(s):  
A. V. Bukusheva
Keyword(s):  
Parallel Transport ◽  
Linear Connection ◽  
Contact Metric Manifold ◽  
Almost Contact Metric Structure ◽  
Almost Contact Metric Manifold ◽  
Contact Metric Manifolds ◽  
Almost Contact Metric ◽  
Invariant Submanifolds ◽  
Contact Metric Structure ◽  
Almost Contact Metric Manifolds

Let M be an almost contact metric manifold of dimension n = 2m + 1. The distribution D of the manifold M admits a natural structure of a smooth manifold of dimension n = 4m + 1. On the manifold M, is defined a linear connection that preserves the distribution D; this connection is determined by the interior connection that allows parallel transport of admissible vectors along admissible curves. The assigment of the linear connection is equivalent to the assignment of a Riemannian metric of the Sasaki type on the distribution D. Certain tensor field of type (1,1) on D defines a so-called prolonged almost contact metric structure. Each section of the distribution D defines a morphism of smooth manifolds. It is proved that if a semi-invariant sub­manifold of the manifold M and is a covariantly constant vec­tor field with respect to the N-connection , then is a semi-invariant submanifold of the manifold D with respect to the prolonged almost contact metric structure.

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