Non-isoparametric solutions of the eikonal equation

Details Non-isoparametric solutions of the eikonal equation Non-isoparametric solutions of the eikonal equation

2010-09-09

arxiv.org/abs/1009.1842v2

Mathematics

Differential Geometry

Typos corrected. References added. Section Concluding remarks added

Scientific paper

In this paper, we prove that a quartic polynomial solution of the eikonal
equation $|\nabla_x f|^2=16x^{6}$ in $\R{n}$ is either an isoparametric
polynomial or congruent to a polynomial $f=(\sum_{i=1}^n
x_i^2)^2-8(\sum_{i=1}^k x_i^2)(\sum_{i=k+1}^{n} x_i^2)$,
$k=0,1,\...,[\frac{n}{2}]$.

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