Homogeneous hypersurfaces of the four-dimensional Thurston geometries ${\mathrm{Sol}}_1^4$, ${\mathrm{Sol}}_{m,n}^4$ and ${\mathrm{Nil}}^4$

Abstract

In this paper, we focus on the four-dimensional Thurston geometries whose isometry groups are four-dimensional, namely ${\mathrm{Sol}}_1^4$, ${\mathrm{Sol}}_{m,n}^4$ and ${\mathrm{Nil}}^4$. We classify homogeneous hypersurfaces in the above three manifolds.

26 pages. Comments are welcome