Perfect-fluid cosmologies with extra dimensions

We give an analysis of the solutions of the n-dimensional vacuum Einstein equations with a metric in the form of a direct sum of a Friedmann-Robertson-Walker (FRW) metric and a Kasner-type Euclidean metric. The solutions are interpreted as four-dimensional perfect-fluid cosmological FRW models, using the simple ansatz proposed by Ib\'an\ifmmode \tilde{}\else \~{}\fi{}ez and Verdaguer. We first obtain the general solution for flat models. These are perfect-fluid solutions that can be made compatible with contraction of all the extra dimensions. The general compatibility of the field equations is then discussed. It is found that for n>5 both open and closed models admit a range of perfect-fluid solutions whose qualitative behavior is analyzed.