C^5中六维完全非退化CR流形的全纯标准型
Holomorphic normal forms of six-dimensional totally nondegenerate CR manifolds in C^5
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中文总结 AI 辅助
针对C^5中由非零对(a,b)参数化的六维完全非退化CR子流形，采用等变活动标架法构造出14个双全纯不等价子类的标准型，确定其无穷小CR自同构李代数并证明标准型收敛性。
中文摘要 AI 辅助
C^5中六维完全非退化CR子流形类包含无穷多个模型，由其定义方程中的非零对(a,b)∈C×R参数化。利用等变活动标架法，我们构造该类的标准型，所得归一化结果分为14个双全纯不等价子类，各有其标准型；对每个子类确定无穷小CR自同构的李代数，最后利用对合法证明所构造标准型的收敛性。
英文摘要
The class of six-dimensional totally nondegenerate CR submanifolds in $\mathbb C^5$ contains an infinite number of models parameterized by nonzero pairs $(a, b)\in\mathbb C\times\mathbb R$ appearing in their defining equations. Employing the equivariant moving frame method, we construct normal forms of this class. The applied normalizations yield into fourteen biholomorphically inequivalent subclasses, each with its own normal form. For each subclass, we determine the Lie algebra of infinitesimal CR automorphisms. Finally, using the method of involution, we prove the convergence of the constructed normal forms.
发表机构
- University of Isfahan（伊斯法罕大学）
- Institute for Research in Fundamental Sciences (IPM)（基础科学研究院）
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