General frame structures on quantum principal bundles

A noncommutative-geometric generalization of the classical formalism of frame bundles is developed, incorporating into the theory of quantum principal bundles the concept of the Levi-Civita connection. The construction of a natural differential calculus on quantum principal frame bundles is presented, including the construction of the associated differential calculus on the structure group. General torsion operators are defined and analyzed. Illustrative examples are presented.