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 between the Riemannian connection and the quarter-symmetric metric connection on a -dimensional quasi-Sasakian manifold. We investigate the curvature tensor and the Ricci tensor of a -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 characterized −projectively flat and −projectively flat -dimensional quasi-Sasakian manifold with respect to the quarter-symmetric metric connection. Finally we study locally −symmetric -dimensional quasi-Sasakian manifold with respect to the quarter-symmetric metric connection.
Acknowledgement
The authors are thankful to the referee for his comments and valuable suggestions towards the improvement of this paper.
Citation
Uday Chand De. Abul Kalam Mondal. "Quarter-symmetric metric connection on -dimensional quasi-Sasakian manifolds." SUT J. Math. 46 (1) 35 - 52, January 2010. https://doi.org/10.55937/sut/1280431052
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