标题： 精确的$(1 + 3 + 6)$维宇宙学型解在包含杨-米尔斯场、高斯-博内项和$Λ$项的引力模型中 显示英文标题

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

摘要： 我们考虑具有$SO(6)$个规范场、高斯-博内项和$\Lambda$项的$10$维引力模型。 我们研究定义在乘积流形$M = R \times R^3 \times K$上的所谓宇宙学类型解，其中$K$是$6d$个卡拉比-丘流形。 通过将规范场1-形式与$K$上的1-形式旋量连接相重合，我们得到了具有标度因子指数依赖性的精确宇宙学解（关于$t$变量），由两个不重合的类似哈勃参数：$H >0$，$h$，遵循$ H + 2 h \neq 0$。 我们还给出了这些宇宙学解的静态类比（对于 $H \neq 0$, $h \neq H$ 和 $ H + 2 h \neq 0$）。两类解的稳定区域已概述。 显示英文摘要

摘要： We consider $10$-dimensional gravitational model with $SO(6)$ Yang-Mills field, Gauss-Bonnet term and $\Lambda$-term. We study so-called cosmological type 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 be coinciding with 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: $H >0$, $h$, 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 stability for both classes of solutions are outlined.