Sections of polar actions

2021/11/09 by Lorenzo-Naveiro, Juan Manuel, Solonenko, Ivan
#53C40 (Primary) #57S25 (Secondary) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2111.05280

Abstract

In this short note we provide an elementary proof of the folklore result in the theory of isometric Lie group actions on Riemannian manifolds asserting that sections of polar actions are totally geodesic.

Related

• Polar actions with a fixed point
• Polar manifolds and actions
• Topics in polar actions
• Introduction to Lie groups, isometric and adjoint actions and some\n generalizations
• Geometric resolution of singular Riemannian foliations