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Article

DEY, Santu ; BHATTACHARYYA, Arindam
Some Properties of Lorentzian $\alpha $-Sasakian Manifolds with Respect to Quarter-symmetric Metric Connection. (English). Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, vol. 54 (2015), issue 2, pp. 21-40
MSC: 53C15, 53C25 | MR 3469689 | Zbl 1346.53032
Keywords:
Quarter-symmetric metric connection; Lorentzian $\alpha $-Sasakian manifold; generalized recurrent manifold; generalized Ricci-recurrent manifold; weakly symmetric manifold; weakly Ricci-symmetric manifold; semi-generalized recurrent manifold; Einstein manifold
Summary:
The aim of this paper is to study generalized recurrent, generalized Ricci-recurrent, weakly symmetric and weakly Ricci-symmetric, semi-generalized recurrent, semi-generalized Ricci-recurrent Lorentzian $\alpha $-Sasakian manifold with respect to quarter-symmetric metric connection. Finally, we give an example of 3-dimensional Lorentzian $\alpha $-Sasakian manifold with respect to quarter-symmetric metric connection.
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