A Study of Trans-Sasakian Manifold Admitting Semi-Symmetric Non-Metric Connection With R.̃S̃=0

Abhishek Singh

doi:https://doi.org/10.14445/22315373/IJMTT-V30P520

International Journal of Mathematics Trends and Technology

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Volume 30 | Number 2 | Year 2016 | Article Id. IJMTT-V30P520 | DOI : https://doi.org/10.14445/22315373/IJMTT-V30P520

A Study of Trans-Sasakian Manifold Admitting Semi-Symmetric Non-Metric Connection With R.̃S̃=0

Abhishek Singh

Abstract

In a trans-Sasakian manifold with R.̃S̃ =0, the Ricci tensors admitting semi-symmetric non-metric connection and admitting Levi-civita connection has been found. It has been proved that a β - Kenmotsu manifold admitting semi-symmetric non-metric connection satisfying R.̃S̃ =0 is an Einstein manifold with constant negative scalar curvature-2n(2n+1)β2.

Keywords

semi-symmetric non-metric connection, Levi-civita connection, trans-Sasakian manifold, Ricci tensor, Einstein manifold.

References

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Citation :

Abhishek Singh, "A Study of Trans-Sasakian Manifold Admitting Semi-Symmetric Non-Metric Connection With R.̃S̃=0," International Journal of Mathematics Trends and Technology (IJMTT), vol. 30, no. 2, pp. 109-114, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V30P520