There is considered the problem of describing up to linear conformal equivalence those harmonic cubic homogeneous polynomials for which the squared-norm of the Hessian is a nonzero multiple of the quadratic form defining the Euclidean metric. Solutions are constructed in all dimensions and solutions are classified in dimension at most 4. Techniques are given for determining when two solutions are linearly conformally inequivalent.

中文翻译：

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调和三次齐次多项式，使得黑森州的范数平方是欧几里德二次形式的倍数

认为存在这样的问题，即描述那些线性三次等式多项式，这些三次三次式多项式的Hessian平方范数是定义欧几里德度量的二次形式的非零倍。在所有维度上构造解，并且在维度上最多分类4个解。给出了确定两个解何时线性共形不等式的技术。