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

Year 2016, Volume: 4 Issue: 4, 276 - 284, 31.12.2016

Tolga Demirli Cumali Ekici , Ali Gorgulu

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.

Keywords

Kenmotsu manifolds, Ricci solitons

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