Geometry of almost Kenmotsu Hom-Lie algebras

Abstract

In the present paper, we introduce left-invariant (almost) Kenmotsu structures on Hom-Lie groups (or, almost Kenmotsu Hom-Lie algebras). Also, we present examples of such structures. It is proved that if the Ricci tensor of Kenmotsu Hom-Lie algebras is η-parallel, then the scalar curvature is constant. We describe η-Einstein Kenmotsu Hom-Lie algebras. Then we show that an involutive Kenmotsu Hom-Lie algebra is not Einstein if it carries Ricci-semisymmetric property. We illustrate that the provide examples support the main results of this paper.