Tbilisi Mathematical Journal

Indefinite trans-Sasakian manifold with semi-symmetric metric connection

Rajendra Prasad and Sushil Kumar

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Abstract

The objective of the present paper is to study of indefinite trans-Sasakian manifold with a semi-symmetric metric connection. We have found the relations between curvature tensors, Ricci curvature tensors and scalar curvature of indefinite trans-Sasakian manifolds with semi-symmetric metric connection and with metric connection. Also, we have proved some results on quasi-projectively flat and $\varphi -$projectively flat manifolds with respect to semi-symmetric metric connection. It is shown that the manifold satisfying $\overset{\_}{R.}\overset{\_}{S}$ $=0$ is an $\eta -$Einstein manifold if $\alpha =0$ and $\beta =constant.$ It is also proved that the manifold satisfying $\overset{\_}{P}.\overset{\_}{S}=0$ is an $\eta -$ Einstein manifold if $\alpha =0$ and $\beta =constant.$ Finally, we have obtained the conditions for the manifold with semi-symmetric metric connection to be conformally flat and $\xi -$conformally flat.

Article information

Source
Tbilisi Math. J., Volume 8, Issue 2 (2015), 233-255.

Dates
Received: 5 July 2015
Accepted: 15 September 2015
First available in Project Euclid: 12 June 2018

Permanent link to this document
https://projecteuclid.org/euclid.tbilisi/1528769020

Digital Object Identifier
doi:10.1515/tmj-2015-0025

Mathematical Reviews number (MathSciNet)
MR3420407

Zentralblatt MATH identifier
1328.53055

Subjects
Primary: 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.)
Secondary: 53C50: Lorentz manifolds, manifolds with indefinite metrics

Keywords
Semi-symmetric metric connection Curvature tensor Ricci-curvature tensor

Citation

Prasad, Rajendra; Kumar, Sushil. Indefinite trans-Sasakian manifold with semi-symmetric metric connection. Tbilisi Math. J. 8 (2015), no. 2, 233--255. doi:10.1515/tmj-2015-0025. https://projecteuclid.org/euclid.tbilisi/1528769020


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