Connection in a tangent bundle to the frame bundle of manifold
... расслоениях // Итоги науки и техн. Современ. пробл. Геометрии / ВИНИТИ. М., 1983. Т. 15. С. 61—93.
6. Do Carmo M. 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