Geodesic
Some Properties of Lorentzian $\alpha $-Sasakian Manifolds with Respect to Quarter-symmetric Metric Connection
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 54 (2015) no. 2, pp. 21-40.

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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.
Classification : 53C15, 53C25
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 
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DEY, Santu; BHATTACHARYYA, Arindam. Some Properties of Lorentzian $\alpha $-Sasakian Manifolds with Respect to Quarter-symmetric Metric Connection. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 54 (2015) no. 2, pp. 21-40. http://geodesic.mathdoc.fr/item/AUPO_2015__54_2_a1/