A note on isoparametric polynomials
classification
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math.DG
keywords
polynomialcartan-mchebychevcompositioneitherevenhomogeneousisoparametric
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We show that any homogeneous polynomial solution of |\nabla F(x)|^2=m^2|x|^(2m-2), m>1, is either a radially symmetric polynomial F(x)=\pm |x|^m (for even m's) or it is a composition of a Chebychev polynomial and a Cartan-M\"unzner polynomial.
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