Some classes of Lorentzian α-Sasakian manifolds with respect to quarter-symmetric metric connection.

S. Dey, B. Pal, A. Bhattacharyya

The object of the present paper is to study a quarter-symmetric metric connection in a Lorentzian α-Sasakian manifold. We study some curvature properties of Lorentzian α-Sasakian manifold with respect to quarter-symmetric metric connection. We investigate quasi-projectively flat, φ-symmetric, φ-projectively flat Lorentzian α-Sasakian manifolds with respect to quarter-symmetric metric connection. We also discuss Lorentzian α-Sasakian manifold admitting quarter-symmetric metric connection satisfying P.S = 0, where P denote the projective curvature tensor with respect to quarter-symmetric metric connection. 

Tbilisi Mathematical Journal, Vol. 10(4) (2017), pp. 1-16