(^-L_n,g)-spaces. Length of a vector field and the angle between two   vector fields
  The notions of length of a vector field and cosine of the angle between two vector fields over a differentiable manifold with contravariant and covariant affine connections and metrics are introduced and considered. The change of the length of a vector field and of the angle between two vector fields along a contravariant vector field are found. The introduced notions are necessary for investigations of different types of transports over a manifold of the above mentioned type. 
S. Manoff