A generalization of Cartan's theorem on isoparametric cubics

Details A generalization of Cartan's theorem on isoparametric cubics A generalization of Cartan's theorem on isoparametric cubics

2010-01-14

arxiv.org/abs/1001.2387v2

Mathematics

Differential Geometry

7 pages, corrected typos; to appear in the Proceedings of the AMS

Scientific paper

We give a generalization of the well-known result of E. 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 $x_n^3-3x_n(x_1^2+...+x_{n-1}^2)$, or to one of four exceptional Cartan
cubic polynomials in dimensions $n=5,8,14,26$.

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