Classification of homogeneous hypersurfaces in some noncompact symmetric spaces of rank two

Abstract

We classify, up to isometric congruence, the homogeneous hypersurfaces in the Riemannian symmetric spaces $\mathrm{SL}(3,\mathbb{H})/\mathrm{Sp}(3),\mathrm{SO}(5,\mathbb{C})/\mathrm{SO}(5),$ and ${\mathrm{Gr}}^{\ast }(2,{\mathbb{C}}^{n+4})=\mathrm{SU}(n+2,2)/\mathrm{S}(\mathrm{U}(n+2)\mathrm{U}(2)),n⩾1$.

38 pages. Minor changes. A few misprints corrected, references added

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• Cohomogeneity one actions on symmetric spaces of noncompact type and higher rank