scholarly journals On Generalized D-Conformal Deformations of Certain Almost Contact Metric Manifolds

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 168
Author(s):  
Nülifer Özdemir ◽  
Şirin Aktay ◽  
Mehmet Solgun
Keyword(s):  
Scalar Curvature ◽  
Covariant Derivative ◽  
Kenmotsu Manifolds ◽  
Contact Metric Manifolds ◽  
Almost Contact Metric ◽  
Conformal Deformations ◽  
Almost Contact Metric Manifolds

In this work, we consider almost contact metric manifolds. We investigate the generalized D-conformal deformations of nearly K-cosymplectic, quasi-Sasakian and β -Kenmotsu manifolds. The new Levi–Civita covariant derivative of the new metric corresponding to deformed nearly K-cosymplectic, quasi-Sasakian and β -Kenmotsu manifolds are obtained. Under some restrictions, deformed nearly K-cosymplectic, quasi-Sasakian and β -Kenmotsu manifolds are obtained. Then, the scalar curvature of these three classes of deformed manifolds are analyzed.

scholarly journals Pointwise Slant and Pointwise Semi-Slant Submanifolds in Almost Contact Metric Manifolds

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 985
Author(s):  
Kwang Soon Park
Keyword(s):  
Fundamental Form ◽  
Second Fundamental Form ◽  
Warping Function ◽  
Topological Properties ◽  
Slant Submanifolds ◽  
Kenmotsu Manifolds ◽  
Contact Metric Manifolds ◽  
Almost Contact Metric ◽  
Almost Contact Metric Manifolds

In almost contact metric manifolds, we consider two kinds of submanifolds: pointwise slant, pointwise semi-slant. On these submanifolds of cosymplectic, Sasakian and Kenmotsu manifolds, we obtain characterizations and study their topological properties and distributions. We also give their examples. In particular, we obtain some inequalities consisting of a second fundamental form, a warping function and a semi-slant function.

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 curves in 3-dimensional normal almost contact metric manifolds

2020 ◽  
Vol 18 (01) ◽  
pp. 2150004
Author(s):  
Abdullah Yıldırım
Keyword(s):  
Contact Manifolds ◽  
3 Dimensional ◽  
And Topology ◽  
Contact Metric Manifolds ◽  
Almost Contact Metric ◽  
Almost Contact Metric Manifolds ◽  
Frenet Curves

The characterization of curves plays an important role in both geometry and topology of almost contact manifolds. Olszak found the equation [Formula: see text] on normal almost contact manifolds. The pair [Formula: see text] denotes the type of these manifolds. In this study, we obtained the curvatures of non-geodesic Frenet curves on [Formula: see text]-dimensional normal almost contact manifolds without neglecting [Formula: see text] and [Formula: see text], and provided the results of their characterization. We exemplified these results with examples.

A Study of New Class of Almost Contact Metric Manifolds of Kenmotsu Type

2021 ◽  
Vol 52 ◽  
Author(s):  
Habeeb Abood ◽  
Mohammed Abass
Keyword(s):  
Einstein Manifold ◽  
Kenmotsu Manifold ◽  
New Class ◽  
Direct Sum ◽  
Contact Metric Manifolds ◽  
Riemannian Curvature Tensor ◽  
Almost Contact Metric ◽  
Structure Equations ◽  
Equivalent Conditions ◽  
Almost Contact Metric Manifolds

In this paper, we characterized a new class of almost contact metric manifolds and established the equivalent conditions of the characterization identity in term of Kirichenko’s tensors. We demonstrated that the Kenmotsu manifold provides the mentioned class; i.e., the new class can be decomposed into a direct sum of the Kenmotsu and other classes. We proved that the manifold of dimension 3 coincided with the Kenmotsu manifold and provided an example of the new manifold of dimension 5, which is not the Kenmotsu manifold. Moreover, we established the Cartan’s structure equations, the components of Riemannian curvature tensor and the Ricci tensor of the class under consideration. Further,the conditions required for this to be an Einstein manifold have been determined.

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