摘要：

Isoparametric hypersurfaces offer a rich source of elegant examples of hypersurfaces in Riemannian manifolds, among which homogeneous hypersurfaces play a fundamental role. In this talk, we will focus on the study of isoparametric hypersurfaces in homogeneous Riemannian manifolds. We will present our classification results on homogeneous hypersurfaces and isoparametric hypersurfaces in four-dimensional Thurston geometries.