The generalization of cosmological models of Friedmann type (the t=con
st section is a manifold of constant curvature) to the case of an arbi
trary number a of spatial dimensions with allowance for the Lambda ter
m is considered. Solutions are obtained in the integrable cases, in pa
rticular, for the distinguished value n=2. For n greater than or equal
to 4 it is shown that the qualitative picture of the evolution is clo
se to the ordinary scenario with n=3.