  The (n +1)-dimensional Einstein-Gauss-Bonnet (EGB) model is considered. For
diagonal cosmological metrics, the equations of motion are written as a set of
Lagrange equations with the effective Lagrangian containing two
"minisuperspace" metrics on R^n: a 2-metric of pseudo-Euclidean signature and a
Finslerian 4-metric proportional to the n-dimensional Berwald-Moor 4-metric.
For the case of the "pure" Gauss-Bonnet model, two exact solutions are
presented, those with power-law and exponential dependences of the scale
factors (w.r.t. the synchronous time variable). (The power-law solution was
considered earlier by N. Deruelle, A. Toporensky, P. Tretyakov, and S.
Pavluchenko.) In the case of EGB cosmology, it is shown that for any
non-trivial solution with an exponential dependence of scale factors, a_i(\tau)
= A_i exp(v^i \tau), there are no more than three different numbers among v^1,
..., v^n.
