Kyungpook Mathematical Journal 2009; 49(4): 789-799  
A Class of Lorentzian $alpha -$Sasakian Manifolds
Ahmet Yildiz1, Mine Turan1, Cengizhan Murathan2
1Art and Science Faculty, Department of Mathematics, Dumlupi nar University, K""{u}tahya, Turkey
2Art and Science Faculty, Department of Mathematics, Uludag University, 16059 Bursa, Turkey
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Abstract
In this study we consider $varphi -$conformally flat, $varphi -$% conharmonically flat, $varphi -$projectively flat and $varphi -$% concircularly flat Lorentzian $alpha -$Sasakian manifolds. In all cases, we get the manifold will be an $eta -$Einstein manifold.
Keywords: The Weyl conformal curvature tensor, the conharmoic curvature tensor, the projective curvature tensor, the concircular curvature tensor, Trans-Sasakian manifolds, Lorentzian $alpha -$Sasakian manifolds

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