A Quarter-symmetric Metric Connection on Almost Contact B-metric Manifolds

Abstract

The aim of this paper is to study the notion of a quarter-symmetric metric connection on an almost contact B-metric manifold (M,\varphi,\xi,\eta,g). We obtain the relation between the Levi-Civita connection and the quarter-symmetric metric connection on (M,\varphi,\xi,\eta,g). We investigate the curvature tensor, Ricci tensor and scalar curvature tensor with respect to the quarter-symmetric metric connection. In case the manifold (M,\varphi,\xi,\eta,g) is a Sasaki-like almost contact B-metric manifold, we get some formulas. Finally, we give some examples of a quarter-symmetric metric connection.