Minimal codimension one foliation of a symmetric space by Damek-Ricci spaces

In this article we consider solvable hypersurfaces of the form N exp(RH) with induced metrics in the symmetric space M = SL(3, C)/SU(3), where Ha suitable unit length vector in the subgroup A of the Iwasawa decomposition SL(3, C) = NAK. Since Mis rank 2, A is 2-dimensional and we can parametrize these hypersurfaces via an angle alpha is an element of [-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 is an element of [-pi/2, 0) boolean AND (0, pi/2] admit planes of both negative and positive sectional curvature. Moreover, the symmetric space Madmits a minimal foliation with all leaves isometric to the non-symmetric 7-dimensional Damek-Ricci space. (C) 2020 Elsevier B.V. All rights reserved.