Polar actions on homogeneous 3-spaces

2025/05/09 by Dominguez-Vazquez, Miguel, Ferreira, Tarcios A., Otero, Tomas · 3 citations
#Differential Geometry (math.DG) #FOS: Mathematics #Primary 53C30 #Secondary 53C40

paper · doi:10.48550/arxiv.2505.05898

Abstract

We classify polar isometric actions on simply connected 3-dimensional Riemannian homogeneous spaces, up to orbit equivalence. In particular, we classify extrinsically homogeneous surfaces in such spaces and study the geometry of the orbit foliations of the corresponding cohomogeneity one actions.

Citations

• Classification of cohomogeneity-one actions on symmetric spaces of noncompact type
• Totally geodesic submanifolds and polar actions on Stiefel manifolds
• The index of symmetry of compact naturally reductive spaces
• Tits Geometry and Positive Curvature
• Polar actions with a fixed point
• Curvatures of left invariant metrics on lie groups

Cited by

• Uniqueness of the Bonnet problem in Thurston geometries
• Homogeneous hypersurfaces of the four-dimensional Thurston geometry \rm Sol₀⁴
• Isometric immersions into three-dimensional unimodular metric Lie groups

Related

• Polar manifolds and actions
• Topics in polar actions
• Polar actions on the complex hyperbolic plane
• Polar actions on Hermitian and quaternion-Kähler symmetric spaces
• Codimension two polar homogeneous foliations on symmetric spaces of noncompact type