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Characterizations of the Lorentzian manifolds admitting a type of semi-symmetric metric connection

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Abstract

We set a type of semi-symmetric metric connection on the Lorentzian manifolds. It is proved that a Lorentzian manifold endowed with a semi-symmetric metric \(\rho \)-connection is a GRW spacetime. We also characterize the Ricci semisymmetric Lorentzian manifold and study the solution of Eisenhart problem of finding the second order parallel (skew-)symmetric tensor on Lorentzian manifolds. Finally, we address physical interpretation of some geometric results of our paper.

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Acknowledgements

The authors express their sincere thanks to the anonymous referees for providing the valuable suggestions in the improvement of the paper. The first author acknowledges authority of University of Technology & Applied Sciences-Shinas for their continuous support and encouragement to carry out this research work. The second author was supported by Grant Project No. NRF-2018-R1D1A1B-05040381 from National Research Foundation of Korea.

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Authors and Affiliations

  1. Section of Mathematics, Department of Information Technology, University of Technology and Applied Sciences, P.O. Box 77, 324, Shinas, Oman

    Sudhakar K. Chaubey

  2. Department of Mathematics and RIRCM, Kyungpook National University, Daegu, 41566, Republic of Korea

    Young Jin Suh

  3. Department of Pure Mathematics, University of Calcutta 35, Ballygaunge Circular Road, Kolkata, West Bengal, 700019, India

    Uday Chand De

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  1. Sudhakar K. Chaubey
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Correspondence to Sudhakar K. Chaubey.

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Chaubey, S.K., Suh, Y.J. & De, U.C. Characterizations of the Lorentzian manifolds admitting a type of semi-symmetric metric connection. Anal.Math.Phys. 10, 61 (2020). https://doi.org/10.1007/s13324-020-00411-1

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