Normal Families of Functions and Groups of Pseudoconformal Diffeomorphisms of Quaternion and Octonion Variables

S. V. Lyudkovskii

Contemporary Mathematics. Fundamental Directions, Functional analysis, Tome 18 (2006), pp. 101-164.

Résumé

This paper is devoted to the specific class of pseudoconformal mappings of quaternion and octonion variables. Normal families of such functions are defined and investigated. Four criteria of a family to be normal are proved. Then groups of pseudoconformal diffeomorphisms of quaternion and octonion manifolds are investigated. It is proved that they are finite-dimensional Lie groups for compact manifolds. Their examples are given. Many characteristic features are found in comparison with commutatiive geometry over $\mathbf R$ or $\mathbf C$.

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