  A D-dimensional cosmological model with several scalar fields and
antisymmetric (p+2)-form is considered. For dimensions D = 4m+1 = 5, 9, 13, ...
and p = 2m-1 = 1, 3, 5, ... we obtain a family of new cosmological type
solutions with 4m-dimensional oriented Ricci-flat submanifold N of Euclidean
signature. These solutions are characterized by a self-dual or anti-self-dual
parallel charge density form Q of rank 2m defined on N. The (sub)manifold N may
be chosen to be K\ddot{a}hler, or hyper-K\ddot{a}hler one, or 8-dimensional
manifold of Spin(7) holonomy. The generalization of solutions to a chain of
extra marginal) Ricci-flat factor-spaces is also presented. Solutions with
accelerated expansion of extra factor-spaces are singled out. Certain examples
of new solutions for IIA supergravity and for a chain of B_D-models in
dimensions D = 14, 15, ... are considered.
