Five-Dimensional Tangent Vectors in Space-Time: V. Generalization of   Covariant Derivative
  In this part of the series I discuss the five-vector generalizations of affine connection and gauge fields. I also give definition to the exterior derivative of nonscalar-valued five-vector forms and consider the five-vector analogs of the field strength tensor. In conclusion I discuss the nonspacetime analogs of five-vectors. 
Alexander Krasulin