  We consider a D-dimensional model of gravity with non-linear "scalar fields"
as a matter source. The model is defined on the product manifold M, which
contains n Einstein factor spaces. General cosmological type solutions to the
field equations are obtained when n-1 factor spaces are Ricci-flat, e.g. when
one space M_1 of dimension d_1 > 1 has nonzero scalar curvature. The solutions
are defined up to solutions to geodesic equations corresponding to a sigma
model target space. Several examples of sigma models are presented. A subclass
of spherically-symmetric solutions is studied and a restricted version of
"no-hair theorem" for black holes is proved. For the case d_1 =2 a subclass of
latent soliton solutions is singled out.
