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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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.


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

Article information

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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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  • C. S. Bagewadi, D. G. Prakasha and Venkatesha., A Study of Ricci quarter-symmetric metric connection on a Riemannian manifold, Indian J. Math., 50 (2008), no. 3, 607-615.
  • E. Boeckx, P. Buecken, and L. Vanhecke, $\phi$-symmetric contact metric spaces, Glasgow Math.J., 41 (1999), 409-416.
  • S. Dey and A. Bhattacharyya, Some Properties of Lorentzian a-Sasakian Manifolds with Respect to Quarter-symmetric Metric Connection, Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Vol. 54 (2015), No. 2, 21–40.
  • A. Friedmann and J. A. Schouten. Uber die Geometrie der halbsymmetrischen Uber-tragung. Math. Zeitschr, 21:211-223, 1924.
  • S. Golab. On semi-symmetric and quarter-symmetric linear connections, Tensor, N.S. 29 (1975) 249-254.
  • H. A. Hayden. Subspaces of a space with torsion. Proc. London Math. Soc., 34:27-50, 1932.
  • R. S. Mishra and S. N. Pandey, On quarter-symmetric metric F-connection, Tensor, N.S. 34 (1980) 1-7.
  • C. Patra and A. Bhattacharyya, Quarter-symmetric metric connection on pseudosymmetric Lorentzian $\alpha$-Sasakian manifolds. International J. Math. Combin. Vol.1 (2013), 46-59.
  • D. G. Prakasha, C. S. Bagewadi and N. S. Basavarajappa, On pseudosymmetric Lorentzian $\alpha$-Sasakian manifolds, IJPAM, Vol. 48, No.1, 2008, 57-65.
  • S. C. Rastogi, On quarter-symmetric connection, C.R. Acad. Sci. Bulgar 31 (1978) 811-814.
  • S. C. Rastogi, On quarter-symmetric metric connection, Tensor 44 (1987) 133-141.
  • T. Takahashi, Sasakian $\phi$-symmetric spaces, Tohoku Math. J. 29 (1977), 91-113.
  • K. Yano. On semi-symmetric metric connections. Rev. Roumaine Math. Pures Appl., 15:1579-1586, 1970.
  • K. Yano and T. Imai, Quarter-symmetric metric connections and their curvature tensors, Tensor, N.S. 38 (1982) 13-18.
  • A. Yildiz and C. Murathan, On Lorentzian $\alpha$-Sasakian manifolds. Kyungpook Math. J. 45 (2005), 95-103.
  • S. Yadav and D. L. Suthar, Certain derivation on Lorentzian $\alpha$-Sasakian manifolds. Mathematics and Decision Science 12 (2012).
  • A. Yildiz, M. Turan and B. F. Acet, On three dimensional Lorentzian $\alpha$-Sasakian manifolds, Bulletin of Mathematical Analysis and Applications, Vol. 1, Issue 3(2009), pp. 90-98.