Harmonic cubic homogeneous polynomials such that the norm-squared of the Hessian is a multiple of the Euclidean quadratic form
arXiv:1905.00071 · doi:10.1007/s13324-020-00462-4
Abstract
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 . Techniques are given for determining when two solutions are linearly conformally inequivalent.
arXiv commentv5: A nowhere used stupidity in the statement of Lemma 6.1 is corrected. This has no effect on other claims. v4: Correction to published version (although Lemma 6.14 was correct as stated, the proof given for it was trivially wrong.)
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