In this article we consider solvable hypersurfaces of the form $N\exp (\mathbb{R}H)$ with induced metrics in the symmetric space $M=SL(3,\mathbb{C})/SU(3)$, where H a suitable unit length vector in the subgroup A of the Iwasawa decomposition $SL(3,\mathbb{C})=NAK$. Since M is rank 2, A is 2-dimensional and we can parametrize these hypersurfaces via an angle $\alpha \in [-\pi /2,\pi /2]$ determining the direction of H. We show that one of the hypersurfaces (corresponding to $\alpha =0$) is minimally embedded and isometric to the non-symmetric 7-dimensional Damek-Ricci space. We also provide an explicit formula for the Ricci curvatures of these hypersurfaces and show that all hypersurfaces for $\alpha \in [-\frac{\pi }{2},0)\cap (0,\frac{\pi }{2}]$ admit planes of both negative and positive sectional curvature. Moreover, the symmetric space M admits a minimal foliation with all leaves isometric to the non-symmetric 7-dimensional Damek-Ricci space.

在本文中，我们考虑以下形式的可解超曲面 $ñ\mathrm{经验值}（\mathbb{[R}H）$ 在对称空间中引入度量 $\mathrm{中号}=\mathrm{小号}\mathrm{大号}（3，\mathbb{C}）/\mathrm{小号}ü（3）$，其中H是Iwasawa分解的子组A中合适的单位长度向量$\mathrm{小号}\mathrm{大号}（3，\mathbb{C}）=ñ\mathrm{一种}ķ$。由于M为2级，A为二维，我们可以通过一个角度对这些超曲面进行参数化$\alpha \in [-\pi /2，\pi /2]$确定H的方向。我们表明，超曲面之一（对应于$\alpha =0$）最小嵌入并且与非对称7维Damek-Ricci空间等距。我们还为这些超曲面的Ricci曲率提供了一个明确的公式，并表明所有超曲面$\alpha \in [-\frac{\pi }{2}，0）\cap （0，\frac{\pi }{2}]$允许平面具有负和正的截面曲率。此外，对称空间M允许最小的叶面，所有叶子都与非对称7维Damek-Ricci空间等距。