Semi-Symmetry Properties of $S$-Manifolds Admitting a Quarter-Symmetric Metric Connection

Abstract

In this study $S$-manifolds admitting a quarter-symmetric metric connection naturally related with the $S$-structure are considered and some general results concerning the curvature of such a connection is given. In addition, we prove that an $S$-manifold has constant $f$-sectional curvature with respect to this quarter-symmetric metric connection if and only if has the same constant $f$-sectional curvature with respect to the Riemannian connection. In particular, the conditions of semi-symmetry, Ricci semi-symmetry, and projective semi-symmetry of this quarter-symmetric metric connection are investigated.