  In a number of physically important cases, the nonholonomically
(nonintegrable) constrained Ricci flows can be modelled by exact solutions of
Einstein equations with nonhomogeneous (anisotropic) cosmological constants. We
develop two geometric methods for constructing such solutions: The first
approach applies the formalism of nonholonomic frame deformations when the
gravitational evolution and field equations transform into systems of nonlinear
partial differential equations which can be integrated in general form. The
second approach develops a general scheme when one (two) parameter families of
exact solutions are defined by any source-free solutions of Einstein's
equations with one (two) Killing vector field(s). A successive iteration
procedure results in a class of solutions characterized by an infinite number
of parameters for a non-Abelian group involving arbitrary functions on one
variable. We also consider nonlinear superpositions of some mentioned classes
of solutions in order to construct more general integral varieties of the Ricci
flow and Einstein equations depending on infinite number of parameters and
three/ four coordinates on four/ five dimensional (semi) Riemannian spaces.
