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On \({\mathcal {M}}\)-projectively semisymmetric Lorentzian \(\alpha \)-Sasakian manifolds

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Abstract

We consider \({\mathcal {M}}\)-projective curvature tensor on Lorentzian \(\alpha \)- Sasakian manifolds and show that \({\mathcal {M}}\)-projectively semisymmetric Lorentzian \(\alpha \)-Sasakian manifold is \({\mathcal {M}}\)-projectively flat. Further, it is shown that, \({\mathcal {M}}\)-projectively semisymmetric Lorentzian \(\alpha \)-Sasakian manifold is semisymmetric. Finally, some results related to energy momentum tensor satisfying the Einstein field equation with cosmological constant of the \({\mathcal {M}}\)-projectively semisymmetric Lorentzian \(\alpha \)-Sasakian space-times are investigated.

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Acknowledgements

The first author (DGP) is thankful to University Grants Commission, New Delhi, India, for financial support in the form of UGC-SAP-DRS-III Programme to the Department of Mathematics, Karnatak University, Dharwad. Also, the third author (VC) is thankful to University Grants Commission, New Delhi, India, for financial support in the form of Rajiv Gandhi National fellowship (F1-17.1/2013-14/RGNF-2013-14-SC-KAR-46330).

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Authors and Affiliations

  1. Department of Mathematics, Karnatak University, Dharwad, 580003, India

    D. G. Prakasha & Vasant Chavan

  2. Department of Mathematics, Istanbul Technical University, Istanbul, Turkey

    F. O. Zengin

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  1. D. G. Prakasha
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  2. F. O. Zengin
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  3. Vasant Chavan
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Correspondence to D. G. Prakasha.

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Prakasha, D.G., Zengin, F.O. & Chavan, V. On \({\mathcal {M}}\)-projectively semisymmetric Lorentzian \(\alpha \)-Sasakian manifolds. Afr. Mat. 28, 899–908 (2017). https://doi.org/10.1007/s13370-017-0493-9

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  • DOI: https://doi.org/10.1007/s13370-017-0493-9

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