Homogeneous hypersurfaces of the four-dimensional Thurston geometry $\mathrm{So}{\mathrm{l}}_0^4$

Abstract

In this paper, we classify hypersurfaces with constant principal curvatures in the four-dimensional Thurston geometry $\mathrm{So}{\mathrm{l}}_0^4$ under certain geometric conditions. As an application of the classification result, we give a complete classification of homogeneous hypersurfaces in $\mathrm{So}{\mathrm{l}}_0^4$, which solves a problem raised by Erjavec and Inoguchi (Problem 6.4 of [J. Geom. Anal. 33, Art. 274, (2023)]).

18 pages. Comments are welcome