CoKahler and Cosymplectic Hom-Lie Algebras

The purpose of this study is to introduce the (almost) cosymplectic Hom-Lie algebras and to show that these Hom-Lie algebras and symplectic Hom-Lie algebras are related to each other. We also describe the notion of the almost coKahler structures on Hom-Lie algebras and show that they are related to almost Kahler structures. The properties of the curvature tensor of such structures are presented in this study. eta-Einstein almost coKahler Hom-Lie algebras are described as well. We give the notions of Hom-eta-parallel and Hom-cyclic parallel. Finally, some conditions for an almost Kahler structure induced by an almost coKahler Hom-Lie algebra to be totally geodesic are given.