Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

A generalization of Cartan's theorem on isoparametric cubics

Author(s): Vladimir G. Tkachev
Journal: Proc. Amer. Math. Soc. 138 (2010), 2889-2895.
MSC (2010): Primary 53C42, 35F20, 17A35; Secondary 15A63, 17A75
Posted: March 29, 2010
MathSciNet review: 2644901
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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 $\vert\nabla f\vert^2=9\vert x\vert^4$ 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 .

References:

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