On the synectic metric in the tangent bundle of a Riemannian manifold

Abstract: The purpose of this paper is to investigate applications the covariant derivatives of the covector fields and killing vector fields with respect to the synectic lift a in a the Riemannian manifold to its tangent bundle, where Cg-complete lift of the Riemannian metric, Va-vertical lift of the symmetric tens field of type (0,2) in Mn .