Connection in a tangent bundle to the frame bundle of manifold
... vectors of this bundle are con-structed. A coordinate representation of the non-holonomic frame vectors is produced. Horizontal and vertical curvatures, torsions, and covariant derivatives are constructed in a homogeneous connection.
Бишоп Р., Криттенден Р. Геометрия ... ... Differential forms and applications. Berlin, Heidelberg, 1994.
Polyakova K.
2nd order tangent bundle, horizontal, vertical and mixed curvatures and torsions, horizontal and vertical covariant derivatives.
106-111