Step-fibred spaces

A class of fibred spaces is introduced, having a fibred space as the base and the stationary subgroup of a supporting $G$-object ($G$ being a Lie group) as the type fibre. The construction of these spaces, named fibred spaces of $H$-structure, is based on properly defined class of Pfaffian systems (systems of step-fibred structure), principal two-floor step-fibred spaces and generalized geometric elements. Various fields of geometrical objects defined on a fibred space of $H$-structure are studied.