New Method for Building Geodesic Lines in Riemann Geometry
  New perspective form of equations for geodesic lines in Riemann Geometry was found. This method is based on the use of differential forms in differential equations as arguments of differentiation. At that, these forms do not have a requirement of completeness, and that extends capabilities of equation transformation, makes their writing very flexible and extend their scope of application. 
Victor I. Pogorelov
math.GM