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.

中文翻译：

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幺正变换下的不变量调和多项式

摘要

研究了三个复变量中实值调和四次多项式族的酉变换和规范代表。该主题涉及对四维复空间的实超曲面和此类曲面的各向同性群（全纯稳定器）的 Moser 法线方程的研究。特定严格伪凸超曲面的稳定器的维数是通过从其正规方程保留四次多项式的酉子群的维数从上面估计的。