  In the present paper we give a differential geometry formulation of the basic
dynamical principle of the group--algebraic approach \cite{LeS92} --- the
grading condition --- in terms of some holomorphic distributions on flag
manifolds associated with the parabolic subgroups of a complex Lie group; and a
derivation of the corresponding nonlinear integrable systems, and their general
solutions. Moreover, the reality condition for these solutions is introduced.
For the case of the simple Lie groups endowed with the canonical gradation,
when the systems in question are reduced to the abelian Toda equations, we
obtain the generalised Pl\"ucker representation for the pseudo--metrics
specified by the K\"ahler metrics on the flag manifolds related to the maximal
nonsemisimple parabolic subgroups; and the generalised infinitesimal Pl\"ucker
formulas for the Ricci curvature tensors of these pseudo--metrics. In
accordance with these formulas, the fundamental forms of the pseudo--metrics
and the Ricci curvature tensors are expressed directly in terms of the abelian
Toda fields, which have here the sense of K\"ahler potentials.
