Abstract <p> Homogeneous model submanifolds of <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11006_2025_3044_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="25" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathrm{CR}\)</EquationSource> </InlineEquation>-type <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11006_2025_3044_Article_IEq4.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="37" /> </InlineMediaObject> <EquationSource Format="TEX">\((1, 3)\)</EquationSource> </InlineEquation> in the complex space <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11006_2025_3044_Article_IEq5.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb C^4\)</EquationSource> </InlineEquation> are investigated. In the course of the study, the moduli space of five-dimensional model surfaces of the Bloom–Graham type <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11006_2025_3044_Article_IEq6.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="136" /> </InlineMediaObject> <EquationSource Format="TEX">\(((2, 1),(3, 1),(4, 1))\)</EquationSource> </InlineEquation> are found. It is also shown that, among the model surfaces of this type, exactly one surface has the property of holomorphic homogeneity, which is equivalent to the tubular surface <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11006_2025_3044_Article_IEq7.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathcal {C}\)</EquationSource> </InlineEquation> over an affinely homogeneous curve in <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11006_2025_3044_Article_IEq8.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb R ^4\)</EquationSource> </InlineEquation>. The paper describes a family of six-dimensional holomorphically homogeneous surfaces obtained as orbits of the action of the group of holomorphic automorphisms of <InlineEquation ID="IEq9"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11006_2025_3044_Article_IEq9.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathcal C\)</EquationSource> </InlineEquation> and classifies them from the point of view of the corresponding model surfaces. </p>

Homogeneous \(\mathrm{CR}\)-Manifolds in \(\mathbb{C}^4\)

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发表日期：

2025年4月1日

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I. I. Zavolokin

摘要

Abstract

Homogeneous model submanifolds of \(\mathrm{CR}\) -type \((1, 3)\) in the complex space \(\mathbb C^4\) are investigated. In the course of the study, the moduli space of five-dimensional model surfaces of the Bloom–Graham type \(((2, 1),(3, 1),(4, 1))\) are found. It is also shown that, among the model surfaces of this type, exactly one surface has the property of holomorphic homogeneity, which is equivalent to the tubular surface \(\mathcal {C}\) over an affinely homogeneous curve in \(\mathbb R ^4\) . The paper describes a family of six-dimensional holomorphically homogeneous surfaces obtained as orbits of the action of the group of holomorphic automorphisms of \(\mathcal C\) and classifies them from the point of view of the corresponding model surfaces.