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.

scholarly journals On δ- Lorentzian trans Sasakian manifold with semi-symmetric metric connection

2021 ◽  
Vol 39 (5) ◽  
pp. 113-135
Author(s):  
Mohd Danish Siddiqi
Keyword(s):  
Scalar Curvature ◽  
Ricci Curvature ◽  
Sasakian Manifold ◽  
Conformally Flat ◽  
Sasakian Manifolds ◽  
Projectively Flat ◽  
Metric Connection ◽  
Flat Manifolds ◽  
Curvature Tensors

The aim of the present research is to study the δ-Lorentzian trans Sasakian manifolds with a semi-symmetric metric connection. We have found the expressions for curvature tensors, Ricci curvature tensors and scalar curvature of the δ-Lorentzian trans Sasakian manifolds with a semi-symmetric metric and metric connection. Also, we have discussed some results on quasi-projectively flat and ϕ-projectively flat manifolds endowed with a semi-symmetric-metric connection. It shown that the manifold satisfying¯R. ¯ S = 0,¯P, ¯ S = 0.Lastly, we have obtained the conditions for the δ-Lorentzian Trans Sasakian manifolds with a semi-symmetric metric connection to be conformally flat and ξ-conformally flat.

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 Results on Weakly Symmetric Kenmotsu Manifolds

2019 ◽  
Vol 7 (1) ◽  
pp. 13-21
Author(s):  
J. P. Singh ◽  
◽  
K. Lalnunsiami
Keyword(s):  
Kenmotsu Manifold ◽  
Kenmotsu Manifolds ◽  
Metric Connection ◽  
Weakly Symmetric ◽  
Symmetric Properties

In this paper, we investigate weakly symmetric, weakly Ricci symmetric, weakly concircular symmetric and weakly concircular Ricci symmetric properties of a Kenmotsu manifold admitting a semi-symmetric metric connection. Some results on weakly -projectively symmetric Kenmotsu manifold with respect to a semi-symmetric metric connection are obtained. An example of a weakly symmetric and weakly Ricci symmetric Kenmotsu manifold with respect to this connection is constructed.

scholarly journals On the quasi-conformal curvature tensor of an almost Kenmotsu manifold with nullity distributions

2018 ◽  
Vol 33 (2) ◽  
pp. 255
Author(s):  
Dibakar Dey ◽  
Pradip Majhi
Keyword(s):  
Vector Field ◽  
Curvature Tensor ◽  
Conformally Flat ◽  
Kenmotsu Manifold ◽  
Conformal Curvature ◽  
Conformal Curvature Tensor ◽  
Kenmotsu Manifolds ◽  
Almost Kenmotsu Manifolds ◽  
Nullity Distribution ◽  
Characteristic Vector Field

The object of the present paper is to characterize quasi-conformally flat and $\xi$-quasi-conformally flat almost Kenmotsu manifolds with  $(k,\mu)$-nullity and $(k,\mu)'$-nullity distributions respectively. Also we characterize almost Kenmotsu manifolds with vanishing extended quasi-conformal curvature tensor and extended $\xi$-quasi-conformally flat almost Kenmotsu manifolds such that the characteristic vector field $\xi$ belongs to the $(k,\mu)$-nullity distribution.

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.

scholarly journals ON PSEUDO CYCLIC RICCI SYMMETRIC MANIFOLDS

2009 ◽  
Vol 02 (02) ◽  
pp. 227-237
Author(s):  
Absos Ali Shaikh ◽  
Shyamal Kumar Hui
Keyword(s):  
Riemannian Manifold ◽  
Einstein Manifold ◽  
Conformally Flat ◽  
Geometric Properties ◽  
Symmetric Manifold ◽  
Euclidean Manifold ◽  
Flat Riemannian Manifold

The object of the present paper is to introduce a type of non-flat Riemannian manifold called pseudo cyclic Ricci symmetric manifold and study its geometric properties. Among others it is shown that a pseudo cyclic Ricci symmetric manifold is a special type of quasi-Einstein manifold. In this paper we also study conformally flat pseudo cyclic Ricci symmetric manifolds and prove that such a manifold can be isometrically immersed in a Euclidean manifold as a hypersurface.

Some classes of Kenmotsu manifolds with respect to semi-symmetric metric connection

2013 ◽  
Vol 29 (7) ◽  
pp. 1311-1322
Author(s):  
D. G. Prakasha ◽  
Aysel Turgut Vanli ◽  
C. S. Bagewadi ◽  
D. A. Patil
Keyword(s):  
Kenmotsu Manifolds ◽  
Metric Connection

scholarly journals η-Ricci Solitons and Gradient Ricci Solitons on f-Kenmotsu Manifolds

2021 ◽  
pp. 19-34
Author(s):  
Mohd Siddiqi
Keyword(s):  
Ricci Solitons ◽  
Gradient Ricci Solitons ◽  
Research Article ◽  
Kenmotsu Manifolds ◽  
Metric Connection

The aim of the present research article is to study the f-kenmotsu manifolds admitting the η-Ricci Solitons and gradient Ricci solitons with respect to the semi-symmetric non metric connection.

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.

Sign in / Sign up

Export Citation Format

Share Document