Exact (1+3+6)-Dimensional Cosmological-Type Solutions in Gravitational Model with Yang-Mills Field, Gauss-Bonnet Term and Λ Term

We consider a 10-dimensional gravitational model with an SO(6)Yang-Mills field, Gauss-Bonnet term, and Lambda term. We study so-called cosmological-type solutions defined on the product manifold M=R x R-3 x K, where K is 6d a Calabi-Yau manifold. By setting the gauge field 1-form to coincide with the 1-form spin connection on K, we obtain exact cosmological solutions with exponential dependence of scale factors (upon t-variable) governed by two non-coinciding Hubble-like parameters: H > 0 and h obeying H+2h not equal 0. We also present static analogs of these cosmological solutions (for H not equal 0, h not equal H, and H+2h not equal 0). The islands of stability for both classes of solutions are outlined.