Tensor-multi-scalar theories from multidimensional cosmology

Inhomogeneous multidimensional cosmological models with a higher dimensional space-time manifold M=M_0 x M_1 x … M_n are investigated under dimensional reduction to tensor-multi-scalar theories. In the Einstein conformal frame, these theories take the shape of a flat sigma-model. For the singular case where M_0 is 2-dimensional, the dimensional reduction to dilaton gravity is preformed with different distinguished representations of the action.