Variationally complete representations are polar (Q2731943)

An action of a compact subgroup \(G\) of the Lie group \(SO(n)\) on \({\mathbb R}^n\) is called variationally complete if any Jacobi field which is generated by variations of geodesics transversal to orbits and tangent to orbits at two points is the restriction of a Killing field induced by the \(G\)-action. An action of \(G\) is called polar if there is an affine subspace which meets all \(G\)-orbits orthogonally. The authors give a new proof to the recent theorem by Gorodski and Thorbergson stating that a variationally complete action of a compact group \(G \subset SO(n)\) is polar.