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December 2015 Indefinite trans-Sasakian manifold with semi-symmetric metric connection
Rajendra Prasad, Sushil Kumar
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Tbilisi Math. J. 8(2): 233-255 (December 2015). DOI: 10.1515/tmj-2015-0025

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.

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Rajendra Prasad. Sushil Kumar. "Indefinite trans-Sasakian manifold with semi-symmetric metric connection." Tbilisi Math. J. 8 (2) 233 - 255, December 2015. https://doi.org/10.1515/tmj-2015-0025

Information

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

zbMATH: 1328.53055
MathSciNet: MR3420407
Digital Object Identifier: 10.1515/tmj-2015-0025

Subjects:
Primary: 53C25
Secondary: 53C50

Rights: Copyright © 2015 Tbilisi Centre for Mathematical Sciences

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Vol.8 • No. 2 • December 2015
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