About horizontally vector lifts of tensor fields from the base to its tangent bundle
The vector field of the type , obtained fr om the tensor field on a smooth manifold M to the tangent bundle , arises in the study of infinitesimal affine transformations with a complete lift. The H-lift was introduced S. Tanno in 1974 in infinitesimal isometries on the tangent bundle with the complete lift. The definition of H’-lift given by ...