Symmetric cotangent bundles of spaces (Q913272)

The structural equations of cotangent bundles \(T^*(V_ n)\) with linear and induced affine connections are pointed out. It is proved that in the symmetric case, if the covariant differentials of the torsion tensor and all curvature tensors are zero, there exists a Lie group the structural constants of which are determined by the curvature object of the space \(T^*(V_ n)\). This group is isomorphic with the group of motions of the \(T^*(V_ n)\).