正规族函数与四元数和八元数伪共形同态群
Normal families of functions and groups of pseudoconformal diffeomorphisms of quaternion and octonion variables
摘要：
本文研究了一类特殊的四元数和八元数的伪共形映射。定义并研究了函数的正规族。证明了一个家庭正常的四个标准。然后研究了四元数流形和八元数流形的伪共形同构群。证明了它们是紧流形的有限维李群。给出了它们的例子。通过与$\bf R$或$\bf C$上的交换几何的比较，发现了它的许多特征.
英文摘要：
This paper is devoted to the specific class of pseudoconformal mappings of quaternion and octonion variables. Normal families of functions are defined and investigated. Four criteria of a family being normal are proven. Then groups of pseudoconformal diffeomorphisms of quaternion and octonion manifolds are investigated. It is proven, that they are finite dimensional Lie groups for compact manifolds. Their examples are given. Many charactersitic features are found in comparison with commutative geometry over $\bf R$ or $\bf C$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
