Linear Transports along Paths in Vector Bundles. II. Some Applications
  The linear transports along paths in vector bundles introduced in Ref. [1] are applied to the special case of tensor bundles over a given differentiable manifold. Links with the transports along paths generated by derivations of tensor algebras are investigated. A possible generalization of the theory of geodesics is proposed when the parallel transport generated by a linear connection is replaced with an arbitrary linear transport along paths in the tangent bundle. 
Bozhidar Z. Iliev (Institute for Nuclear Research and Nuclear Energy,   Bulgarian Academy of Sciences, Sofia, Bulgaria)