Isoparametric surfaces in $\mathbb{E}(\kappa ,\tau )$-spaces

Abstract

We provide an explicit classification of the following four families of surfaces in any homogeneous 3-manifold with 4-dimensional isometry group: isoparametric surfaces, surfaces with constant principal curvatures, homogeneous surfaces, and surfaces with constant mean curvature and vanishing Abresch-Rosenberg differential.

13 pages

References in corpus (2)

• Isoparametric hypersurfaces in complex hyperbolic spaces
• Dual quadratic differentials and entire minimal graphs in Heisenberg space

Cited by in corpus (2)

• Conjugate Plateau constructions in product spaces
• Polar actions on homogeneous 3-spaces