Polar and coisotropic actions on Kähler manifolds (Q2781382)

From the article: The action of a compact Lie group \(G\) of isometries on a Riemannian manifold \((M,g)\) is called polar if there exists a properly embedded submanifold \(\Sigma\) which meets every \(G\)-orbit and is orthogonal to the \(G\)-orbits in all common points. Such a submanifold \(\Sigma\) is called a section [see \textit{R. S. Palais} and \textit{C.-L. Terng}, Trans. Am. Math. Soc. 300, 771-789 (1987; Zbl 0652.57023) and Critical point theory and submanifold geometry, Lect. Notes Math. 1353 (1988; Zbl 0658.49001)] and if it is flat, the action is called hyperpolar. It is of course meaningful to relax the definition of polar actions and not require that the section be properly embedded. The main result of the paper is that a polar action on a compact irreducible homogeneous Kähler manifold is coisotropic. This is then used to give new examples of polar actions and to classify coisotropic and polar actions on quadrics.