Quarter-symmetric metric connection on 3-dimensional quasi-Sasakian manifolds

Abstract

The object of the present paper is to study a quarter-symmetric metric connection on a 3-dimensional quasi-Sasakian manifold. The existence of the connection is given on a Riemannian manifold. We deduce the relation be- tween the Riemannian connection and the quarter-symmetric metric connection on a 3-dimensional quasi-Sasakian manifold. We investigate the curvature ten- sor and the Ricci tensor of a 3-dimensional quasi-Sasakian manifold with respect to the quarter-symmetric metric connection. We study the projective curvature tensor with respect to the quarter-symmetric metric connection and also charac- terized ξ−projectively flat and φ−projectively flat 3-dimensional quasi-Sasakian manifold with respect to the quarter-symmetric metric connection. Finally we study locally φ−symmetric 3-dimensional quasi-Sasakian manifold with respect to the quarter-symmetric metric connection. AMS 2000 Mathematics Subject Classification. 53C15, 53C40.