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We consider $10$-dimensional gravitational model with $SO(6)$ Yang-Millsfield, Gauss-Bonnet term and $\Lambda$-term. We study so-called cosmologicaltype solutions defined on product manifold $M = R \times R^3 \times K$, where$K$ is $6d$ Calabi-Yau manifold. By putting the gauge field 1-form to becoinciding with 1-form spin connection on $K$, we obtain exact cosmologicalsolutions with exponential dependence of scale factors (upon $t$-variable),governed by two non-coinciding Hubble-like parameters: $H >0$, $h$, obeying $ H+ 2 h \neq 0$. We also present static analogs of these cosmological solutions(for $H \neq 0$, $h \neq H$ and $ H + 2 h \neq 0$). The islands of stabilityfor both classes of solutions are outlined.

Exact $(1 + 3 + 6)$-dimensional cosmological-type solutions in gravitational model with Yang-Mills field, Gauss-Bonnet term and $\Lambda$-term