scholarly journals Nearly Sasakian manifolds revisited

2019 ◽  
Vol 6 (1) ◽  
pp. 320-334 ◽  
Author(s):  
Beniamino Cappelletti-Montano ◽  
Antonio De Nicola ◽  
Giulia Dileo ◽  
Ivan Yudin
Keyword(s):  
Sasakian Manifolds ◽  
Contact Metric Manifold ◽  
Almost Contact Metric Manifold ◽  
Conceptual Proof ◽  
Almost Contact Metric ◽  
Nearly Sasakian

AbstractWe provide a new, self-contained and more conceptual proof of the result that an almost contact metric manifold of dimension greater than 5 is Sasakian if and only if it is nearly Sasakian.

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 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.

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.

On ruled surface in 3-dimensional almost contact metric manifold

2017 ◽  
Vol 14 (05) ◽  
pp. 1750076 ◽  
Author(s):  
Murat Kemal Karacan ◽  
Nural Yuksel ◽  
Hasibe Ikiz
Keyword(s):  
Cross Product ◽  
Ruled Surface ◽  
Contact Metric Manifold ◽  
Almost Contact Metric Manifold ◽  
3 Dimensional ◽  
Contact Metric Manifolds ◽  
Special Cases ◽  
Distribution Parameters ◽  
Almost Contact Metric ◽  
Phd Thesis

In this paper, we study ruled surface in 3-dimensional almost contact metric manifolds by using surface theory defined by Gök [Surfaces theory in contact geometry, PhD thesis (2010)]. We also studied the theory of curves using cross product defined by Camcı. In this study, we obtain the distribution parameters of the ruled surface and then some results and theorems are presented with special cases. Moreover, some relationships among asymptotic curve and striction line of the base curve of the ruled surface have been found.

scholarly journals On a semi-symmetric non-metric connection

Filomat ◽  
2011 ◽  
Vol 25 (4) ◽  
pp. 19-27 ◽  
Author(s):  
S.K. Chaubey ◽  
R.H. Ojha
Keyword(s):  
Riemannian Manifold ◽  
Contact Metric Manifold ◽  
Kenmotsu Manifold ◽  
Almost Contact Metric Manifold ◽  
Metric Connection ◽  
Almost Contact Metric

Yano [1] defined and studied semi-symmetric metric connection in a Riemannian manifold and this was extended by De and Senguta [8] and many other geometers. Recently, the present authors [3], [5] defined semi-symmetric non-metric connections in an almost contact metric manifold. In this paper, we studied some properties of a semi-symmetric non-metric connection in a Kenmotsu manifold.

scholarly journals On a semi-symmetric non-metric connection

Filomat ◽  
2012 ◽  
Vol 26 (2) ◽  
pp. 269-275 ◽  
Author(s):  
S.K. Chaubey ◽  
R.H. Ojha
Keyword(s):  
Riemannian Manifold ◽  
Contact Metric Manifold ◽  
Kenmotsu Manifold ◽  
Almost Contact Metric Manifold ◽  
Metric Connection ◽  
Almost Contact Metric

Yano [10] defined and studied semi-symmetric metric connection in a Riemannian manifold and this was extended by De and Senguta [4] and many other geometers. Recently, the present authors [2], [3] defined semi-symmetric non-metric connections in an almost contact metric manifold. In this paper, we studied some properties of a semi-symmetric non-metric connection in a Kenmotsu manifold.

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

Magnetic Trajectories in an Almost Contact Metric Manifold $${\mathbb{R}^{2N+1}}$$ R 2 N + 1

2014 ◽  
Vol 67 (1-2) ◽  
pp. 125-134 ◽  
Author(s):  
Mohamed Jleli ◽  
Marian Ioan Munteanu ◽  
Ana Irina Nistor
Keyword(s):  
Contact Metric Manifold ◽  
Almost Contact Metric Manifold ◽  
Almost Contact Metric
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