Non-isoparametric solutions of the eikonal equation

Abstract

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

Typos corrected. References added. Section Concluding remarks added

References in corpus (1)

• Minimal cubic cones via Clifford algebras