scholarly journals On a type of semisymmetric metric connection on a Riemannian manifold

2015 ◽  
Vol 98 (112) ◽  
pp. 211-218
Author(s):  
Uday De ◽  
Ajit Barman
Keyword(s):  
Riemannian Manifold ◽  
Torsion Tensor ◽  
Symmetric Manifold ◽  
Metric Connection

We study a type of semisymmetric metric connection on a Riemannian manifold whose torsion tensor is almost pseudo symmetric and the associated 1-form of almost pseudo symmetric manifold is equal to the associated 1-form of the semisymmetric metric connection.

scholarly journals Generalized Semi-Symmetric Non-Metric Connections of Non-Integrable Distributions

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 79
Author(s):  
Tong Wu ◽  
Yong Wang
Keyword(s):  
Riemannian Manifold ◽  
Metric Connection

In this work, the cases of non-integrable distributions in a Riemannian manifold with the first generalized semi-symmetric non-metric connection and the second generalized semi-symmetric non-metric connection are discussed. We obtain the Gauss, Codazzi, and Ricci equations in both cases. Moreover, Chen’s inequalities are also obtained in both cases. Some new examples based on non-integrable distributions in a Riemannian manifold with generalized semi-symmetric non-metric connections are proposed.

scholarly journals On Submanifolds in a Riemannian Manifold with a Semi-Symmetric Non-Metric Connection

Symmetry ◽  
2017 ◽  
Vol 9 (7) ◽  
pp. 112 ◽  
Author(s):  
Jing Li ◽  
Guoqing He ◽  
Peibiao Zhao
Keyword(s):  
Riemannian Manifold ◽  
Metric Connection

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.

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.

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