Sections of polar actions
Juan Manuel Lorenzo-Naveiro, Ivan Solonenko
TL;DR
This paper offers a straightforward proof that sections of polar actions in Riemannian geometry are totally geodesic, clarifying a well-known but previously less formalized result.
Contribution
It provides an elementary and rigorous proof of a classical result regarding the nature of sections in polar actions.
Findings
Sections of polar actions are totally geodesic.
Elementary proof simplifies understanding of the folklore result.
Clarifies foundational aspects of isometric Lie group actions.
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.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Advanced Differential Geometry Research