scholarly journals f-Kenmotsu manifolds with the Schouten-van Kampen connection

2017 ◽  
Vol 102 (116) ◽  
pp. 93-105 ◽  
Author(s):  
Ahmet Yıldız
Keyword(s):  
3 Dimensional ◽  
Projectively Flat ◽  
Kenmotsu Manifolds

We study 3-dimensional f-Kenmotsu manifolds with the Schouten-van Kampen connection. With the help of such a connection, we study projectively flat, conharmonically flat, Ricci semisymmetric and semisymmetric 3-dimensional f-Kenmotsu manifolds. Finally, we give an example of 3- dimensional f-Kenmotsu manifolds with the Schouten-van Kampen connection.

scholarly journals Semi-Symmetric Metric Connection on Homothetic Kenmotsu Manifolds

2020 ◽  
Vol 12 (3) ◽  
pp. 223-232
Author(s):  
L. Thangmawia ◽  
R. Kumar
Keyword(s):  
Kenmotsu Manifold ◽  
3 Dimensional ◽  
Projectively Flat ◽  
Kenmotsu Manifolds ◽  
Metric Connection

The object of the paper is to study homothetic Kenmotsu manifold with respect to semi-symmetric metric connection. We discuss locally -symmetric homothetic Kenmotsu manifold and -projectively flat homothetic Kenmotsu manifold with respect to semi-symmetric metric connection. Finally, we construct an example of 3-dimensional homothetic Kenmotsu manifold to verify some results.

scholarly journals Some Symmetric Properties of Kenmotsu Manifolds Admitting Semi-Symmetric Metric Connection

2019 ◽  
pp. 35
Author(s):  
Venkatesha Venkatesh ◽  
Arasaiah Arasaiah ◽  
Vishnuvardhana Srivaishnava Vasudeva ◽  
Naveen Kumar Rahuthanahalli Thimmegowda
Keyword(s):  
Kenmotsu Manifold ◽  
3 Dimensional ◽  
Kenmotsu Manifolds ◽  
Metric Connection ◽  
Symmetric Properties

The object of the present paper is to study some symmetric propertiesof Kenmotsu manifold endowed with a semi-symmetric metric connection. Here weconsider pseudo-symmetric, Ricci pseudo-symmetric, projective pseudo-symmetric and -projective semi-symmetric Kenmotsu manifold with respect to semi-symmetric metric connection. Finally, we provide an example of 3-dimensional Kenmotsu manifold admitting a semi-symmetric metric connection which verify our results.

Almost quasi-Yamabe solitons and gradient almost quasi-Yamabe solitons in f-kenmotsu manifolds

2021 ◽  
pp. 2150180
Author(s):  
Sujit Ghosh ◽  
Uday Chand De
Keyword(s):  
3 Dimensional ◽  
Kenmotsu Manifolds ◽  
Yamabe Solitons

In this paper, we study almost quasi-Yamabe solitons and gradient almost quasi-Yamabe solitons in 3-dimensional [Formula: see text]-Kenmotsu manifolds.

scholarly journals ON φˇ-SEMISYMMETRIC LP-KENMOTSU MANIFOLDS WITH A QSNM-CONNECTION ADMITTING RICCI SOLITONS

2021 ◽  
Vol 45 (5) ◽  
pp. 815-827 ◽  
Author(s):  
RAJENDRA PRASAD ◽  
◽  
RAJENDRA PRASAD ◽  
UMESH KUMAR GAUTAM
Keyword(s):  
Ricci Solitons ◽  
3 Dimensional ◽  
Kenmotsu Manifolds ◽  
Metric Connection

Abstract. In the present work, we characterize Lorentzian para-Kenmotsu (briefly, LP-Kenmotsu) manifolds with a quarter-symmetric non-metric connection (briefly, QSNM-connection) ∇b satisfying certain φ¨-semisymmetric conditions admitting Ricci solitions. At the end of the paper, a 3-dimensional example of LP-Kenmotsu manifolds with a connection ∇b is given to verify some results of the present paper.

scholarly journals On para-Kenmotsu manifolds

Filomat ◽  
2018 ◽  
Vol 32 (14) ◽  
pp. 4971-4980 ◽  
Author(s):  
Simeon Zamkovoy
Keyword(s):  
Sectional Curvature ◽  
Ricci Tensor ◽  
Constant Scalar Curvature ◽  
Holomorphic Sectional Curvature ◽  
Kenmotsu Manifold ◽  
3 Dimensional ◽  
Kenmotsu Manifolds ◽  
Locally Conformally Flat ◽  
Parallel Ricci Tensor ◽  
Negative Sectional Curvature

In this paper we study para-Kenmotsu manifolds. We characterize this manifolds by tensor equations and study their properties. We are devoted to a study of ?-Einstein manifolds. We show that a locally conformally flat para-Kenmotsu manifold is a space of constant negative sectional curvature -1 and we prove that if a para-Kenmotsu manifold is a space of constant ?-para-holomorphic sectional curvature H, then it is a space of constant sectional curvature and H = -1. Finally the object of the present paper is to study a 3-dimensional para-Kenmotsu manifold, satisfying certain curvature conditions. Among other, it is proved that any 3-dimensional para-Kenmotsu manifold with ?-parallel Ricci tensor is of constant scalar curvature and any 3-dimensional para-Kenmotsu manifold satisfying cyclic Ricci tensor is a manifold of constant negative sectional curvature -1.

A note on gradient solitons on para-Kenmotsu manifolds

2020 ◽  
Vol 18 (01) ◽  
pp. 2150007
Author(s):  
Krishnendu De ◽  
Uday Chand De
Keyword(s):  
3 Dimensional ◽  
Kenmotsu Manifolds ◽  
Gradient Solitons

The purpose of the offering exposition is to characterize gradient Yamabe, gradient Einstein and gradient [Formula: see text]-quasi Einstein solitons within the framework of 3-dimensional para-Kenmotsu manifolds. Finally, we consider an example to prove the result obtained in previous section.

scholarly journals On 3-dimensional f-Kenmotsu manifolds and Ricci solitons

2013 ◽  
Vol 65 (5) ◽  
pp. 684-693 ◽  
Author(s):  
A. Yildiz ◽  
U. C. De ◽  
M. Turan
Keyword(s):  
Ricci Solitons ◽  
3 Dimensional ◽  
Kenmotsu Manifolds

scholarly journals On the Classification of Almost Kenmotsu Manifolds of Dimension 3

ISRN Geometry ◽  
2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Yaning Wang ◽  
Ximin Liu
Keyword(s):  
Classification Theorem ◽  
Kenmotsu Manifold ◽  
3 Dimensional ◽  
Almost Kenmotsu Manifold ◽  
Geometric Conditions ◽  
Kenmotsu Manifolds ◽  
Almost Kenmotsu Manifolds ◽  
Weyl Manifold

This paper deals with the classification of a 3-dimensional almost Kenmotsu manifold satisfying certain geometric conditions. Moreover, by applying our main classification theorem, we obtain some suffcient conditions for an almost Kenmotsu manifold of dimension 3 to be an Einstein-Weyl manifold.

scholarly journals Ricci Solitons in β-Kenmotsu Manifolds

2018 ◽  
Vol 56 (1) ◽  
pp. 149-163
Author(s):  
Rajesh Kumar
Keyword(s):  
Vector Field ◽  
Ricci Soliton ◽  
Second Order ◽  
Ricci Solitons ◽  
Kenmotsu Manifold ◽  
Constant Multiple ◽  
Metric Tensor ◽  
3 Dimensional ◽  
Kenmotsu Manifolds

Abstract The object of the present paper is to study Ricci soliton in β-Kenmotsu manifolds. Here it is proved that a symmetric parallel second order covariant tensor in a β-Kenmotsu manifold is a constant multiple of the metric tensor. Using this result, it is shown that if (ℒVg +2S)is ∇-parallel where V is a given vector field, then the structure (g, V, λ) yields a Ricci soliton. Further, by virtue of this result, we found the conditions of Ricci soliton in β-Kenmotsu manifold to be shrinking, steady and expending respectively. Next, Ricci soliton for 3-dimensional β-Kenmotsu manifold are discussed with an example.

scholarly journals Certain results on Lorentzian para-Kenmotsu manifolds

2021 ◽  
Vol 39 (3) ◽  
pp. 201-220
Author(s):  
Abdul Haseeb ◽  
Rajendra Prasad
Keyword(s):  
Einstein Manifold ◽  
Conformally Flat ◽  
Projectively Flat ◽  
Kenmotsu Manifolds ◽  
Metric Connection

The object of the present paper is to study Lorentzian para-Kenmotsu manifolds with respect to the quarter-symmetric metric connection. First we study Lorentzian para-Kenmotsu manifolds with respect to the quarter-symmetric metric connection satisfying the conditions $\bar R\cdot \bar S=0$ and $\bar S\cdot \bar R=0$. After that we study $\phi$-conformally flat, $\phi$-conharmonically flat, $\phi$-concircularly flat, $\phi$-projectively flat and conformally flat Lorentzian para-Kenmotsu manifolds with respect to the quarter-symmetric metric connection and it is shown that in each of these case the manifold is generalized $\eta$-Einstein manifold.

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