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Diagonal lift in the cotangent bundle and its applications. (English) Zbl 1027.53015
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 is defined. Finally the Killing vector fields and geodesics in T * (M n ) with metric D g are described.
MSC:
53A45Vector and tensor analysis
53B21Methods of Riemannian geometry