Diagonal lift in the cotangent bundle and its applications (Q2776893)

The purpose of this paper is to define a diagonal lift \(D_g\) and a Levi-Civita connection of \(T^*(M_n)\) in a natural way and to investigate applications of the diagonal lifts. In the introduction the cotangent bundle \(T^*(M_n)\) over \(M_n\) i.e. an \(n\)-dimensional differentiable manifold of class \(C^\infty\) is defined. Finally the Killing vector fields and geodesics in \(T^*(M_n)\) with metric \(D_g\) are described.