Abstract
The multidimensional cosmological model describing the evolution of n Einstein spaces in the presence of multicomponent perfect fluid is considered. We define vectors related to the equations of state of the components. If they are orthogonal with respect to the minisuperspace metric, the Einstein equations are integrable and a Kasner-like form of the solutions is presented. For special sets of parameters the cosmological model is reduced to the Euclidean Toda-like system connected with some Lie algebra. The integrable vacuum (1+5+5)-model with two 5-dimensional Einstein spaces and non-zero Ricci tensors is obtained. Its reduction to a (1+5+3+2)-solution is given. For a special choice of the integration constant and one of the spaces (M1 = S5) a non-singular solution with the topology \(R^6 \times {\text{ }}M_2\) is obtained.
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