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JMB Journal of Microbiolog and Biotechnology

OPEN ACCESS eISSN 0454-8124
pISSN 1225-6951
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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

Abstract

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