Abstract
Unitary transformations and canonical representatives of a family of real-valued harmonic fourth-degree polynomials in three complex variables are studied. The subject relates to the study of Moser normal equations for real hypersurfaces of four-dimensional complex spaces and isotropy groups (holomorphic stabilizers) of such surfaces. The dimension of the stabilizer for a particular strictly pseudo-convex hypersurface is estimated from above by the dimension of a unitary subgroup preserving the fourth-degree polynomial from its normal equation.
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Translated from Matematicheskie Zametki, 2021, Vol. 109, pp. 856-871 https://doi.org/10.4213/mzm12924.
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Loboda, A.V., Darinskii, B.M. & Kozoriz, D.V. On Harmonic Polynomials Invariant under Unitary Transformations. Math Notes 109, 896–908 (2021). https://doi.org/10.1134/S0001434621050230
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DOI: https://doi.org/10.1134/S0001434621050230