A generalization of Cartan’s theorem on isoparametric cubics

Tkachev, Vladimir

doi:10.1090/S0002-9939-10-10385-2

A generalization of Cartan’s theorem on isoparametric cubics
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by Vladimir G. Tkachev PDF

Proc. Amer. Math. Soc. 138 (2010), 2889-2895 Request permission

Abstract:

We generalize the well-known result of É. Cartan on isoparametric cubics by showing that a homogeneous cubic polynomial solution of the eiconal equation $|\nabla f|^2=9|x|^4$ must be rotationally equivalent to either $x_n^3-3x_n(x_1^2+\ldots +x_{n-1}^2)$ or to one of four exceptional Cartan cubic polynomials in dimensions $n=5,8,14,26$.

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