Some Results on Tangent Bundles with Berger Type Deformed Sasaki Metric over Kählerian Manifolds

Let M be a Kahlerian manifold equipped with an almost complex struc-ture J and a Riemannian metric g, and let TM be its tangent bundle with the Berger type deformed Sasaki metric. In this paper, firstly, we find all forms of Riemannian curvature tensors of TM. Secondly, we search the con-ditions under which a vector field is harmonic with respect to the Berger type deformed Sasaki metric and give some examples of harmonic vector fields. Finally, we study the harmonicity of maps between the Riemannian manifold and the tangent bundle of another Riemannian manifold and vice versa.