Geometric phases and the informational completeness of quantum frames

The basic results on geometric phases are rederived by using infinite dimensional coordinate charts in line bundles, in Hopf bundles, and in projective Hilbert spaces. The determination of a quantum state can be then geometrically described as the measurement of Fubini-Study distances from that state to the elements of informationally complete quantum frames. The basic geometric features of such quantum frames are formulated, and their relationships to corresponding classical frames are analyzed.