Original Article
Kyungpook Mathematical Journal 2005; 45(1): 95-103
Published online March 23, 2005
Copyright © Kyungpook Mathematical Journal.
On Lorentzian $alpha$-Sasakian Manifolds
Ahmet Yildiz1, Cengizhan Murathan2
1Dumlupinar University, Art and Science Faculty, Department of Mathematics, Kutahya, Turkey
2Uludag University, Art and Science Faculty, Department of Mathematics, Bursa, Turkey
he present paper deals with Lorentzian $alpha$-Sasakian manifolds with conformally flat and quasi conformally flat curvature tensor. It is shown that in both cases, the manifold is locally isometric with a sphere $S^{2^n+1} (c)$. Further it is shown that an Lorentzian $alpha$-Sasakian manifold with $R(X,Y).C=0 $ is locally isometric with a sphere $S^{2^n+1}(c)$, where $c=alpha^2$.
Keywords: trans-Sasakian manifolds, $alpha$-Sasakian manifolds, Lorentzian $alpha$-Sasakian manifolds