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arXiv · 1905.00071

Harmonic cubic homogeneous polynomials such that the norm-squared of the Hessian is a multiple of the Euclidean quadratic form

Daniel J. F. Fox
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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 $4$. Techniques are given for determining when two solutions are linearly conformally inequivalent.

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Daniel J. F. Fox. 2019-04-30. Harmonic cubic homogeneous polynomials such that the norm-squared of the Hessian is a multiple of the Euclidean quadratic form. https://doi.org/10.1007/s13324-020-00462-4

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