Tbilisi Mathematical Journal

Some classes of Lorentzian α-Sasakian manifolds with respect to quarter-symmetric metric connection

Santu Dey, Buddhadev Pal, and Arindam Bhattacharyya

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Abstract

The object of the present paper is to study a quarter-symmetric metric connection in a Lorentzian $α$-Sasakian manifold. We study some curvature properties of Lorentzian $α$-Sasakian manifold with respect to quarter-symmetric metric connection. We investigate quasi-projectively at, $\varphi$-symmetric, $\varphi$-projectively at Lorentzian $α$-Sasakian manifolds with respect to quartersymmetric metric connection. We also discuss Lorentzian $α$-Sasakian manifold admitting quarter-symmetric metric connection satisfying $\tilde{P}.\tilde{S} = 0$, where $\tilde{P}$ denote the projective curvature tensor with respect to quarter-symmetric metric connection.

Note

The first author is supported by DST/INSPIRE Fellowship/2013/1041, Govt. of India.

Article information

Source
Tbilisi Math. J., Volume 10, Issue 4 (2017), 1-16.

Dates
Received: 8 November 2016
Accepted: 17 August 2017
First available in Project Euclid: 21 April 2018

Permanent link to this document
https://projecteuclid.org/euclid.tbilisi/1524276053

Digital Object Identifier
doi:10.1515/tmj-2017-0041

Mathematical Reviews number (MathSciNet)
MR3707131

Zentralblatt MATH identifier
1373.53036

Subjects
Primary: 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.)
Secondary: 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.)

Keywords
quarter-symmetric metric connection Lorentzian $α$-Sasakian manifold quasi-projectively flat Lorentzian $α$-Sasakian manifold $\varphi$-symmetric manifold $\varphi$-projectively flat Lorentzian $α$-Sasakian manifold

Citation

Dey, Santu; Pal, Buddhadev; Bhattacharyya, Arindam. Some classes of Lorentzian α-Sasakian manifolds with respect to quarter-symmetric metric connection. Tbilisi Math. J. 10 (2017), no. 4, 1--16. doi:10.1515/tmj-2017-0041. https://projecteuclid.org/euclid.tbilisi/1524276053


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