Lift GD of a Riemannian G to FM

Abstract

Let Γ be a linear connection on M, ∇ its covariant derivative and G a tensor field of type (0,2) on M. In Chapter 5 we have introduced the diagonal lift of tensor fields on M to FM with respect to the connection Γ. Since that lift preserves the type of the tensor, we shall be interested throughout this Chapter initially in those tensors of type (0,2) in general, and later in the important case of the lift of metric tensors, because these will produce Riemannian metrics on FM, and that makes their study specially interesting.