Brouwer degrees of the gradient maps of isoparametric functions
Let \(f:\mathbb{R}^{n+2}\to \mathbb{R}\) be an isoparametric polynomial of degree \(k\) and \(\Phi:\mathbb{R}^{n+2}\to \mathbb{R}^{n+2}\) the associated homogeneous map, \(\Phi={1\over k}\nabla f\). The author studies the relationship between the tangent map of \(\Phi\) and the Hessian of \(f\), finds a certain decomposition of \(f\) and calculates the degree of \(\Phi\).
scientific article; zbMATH DE number 987522