Ricci Solitons in f-Kenmotsu Manifolds with the semi-symmetric non-metric connection

Abstract

In this study, some curvature conditions are given for 3-dimensional f-Kenmotsu manifolds with the semi-symmetric non-metric connection. It is showed that this manifold is not always ξ-projective flat. Moreover, it is informed that if 3-dimensional f-Kenmotsu manifold with the semi-symmetric non-metric connection is Ricci semi-symmetric and regular, then the manifold is an Einstein manifold. Finally, it is proved that 3-dimensional f-Kenmotsu manifold with the semi-symmetric non-metric connection is also an η-Einstein manifold and the Ricci soliton defined on this manifold is named expanding or shrinking with respect to values of f and λ constant.