INTEGRABILITY OF MULTICOMPONENT MODELS IN MULTIDIMENSIONAL COSMOLOGY

The multidimensional cosmological model describing the evolution of n Einstein spaces in the presence of multicomponent perfect fluid is con sidered. We define vectors related to the equations of state of the co mponents. If they are orthogonal with respect to the minisuperspace me tric, the Einstein equations are integrable and a Kasner-like form of the solutions is presented. For special sets of parameters the cosmolo gical model is reduced to the Euclidean Toda-like system connected wit h some Lie algebra. The integrable vacuum (1+5+5)-model with two 5-dim ensional Einstein spaces and non-zero Ricci tensors is obtained. Its r eduction to a (1+5+3+2)-solution is given. For a special choice of the integration constant and one of the spaces (M-1 = S-5) a, non-singula r solution with the topology R-6 X M-2 is obtained.