  The maximally-decoupled method has been considered as a theory to apply an
basic idea of an integrability condition to certain multiple parametrized
symmetries. The method is regarded as a mathematical tool to describe a
symmetry of a collective submanifold in which a canonicity condition makes the
collective variables to be an orthogonal coordinate-system. For this aim we
adopt a concept of curvature unfamiliar in the conventional time-dependent (TD)
self-consistent field (SCF) theory. Our basic idea lies in the introduction of
a sort of Lagrange manner familiar to fluid dynamics to describe a collective
coordinate-system. This manner enables us to take a one-form which is linearly
composed of a TD SCF Hamiltonian and infinitesimal generators induced by
collective variable differentials of a canonical transformation on a group. The
integrability condition of the system read the curvature C=0. Our method is
constructed manifesting itself the structure of the group under consideration.
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