Normal families of functions and groups of pseudoconformal diffeomorphisms of quaternion and octonion variables
Identifieur interne : 000833 ( Main/Exploration ); précédent : 000832; suivant : 000834Normal families of functions and groups of pseudoconformal diffeomorphisms of quaternion and octonion variables
Auteurs : S. V. Ludkovsky [Russie]Source :
- Journal of Mathematical Sciences [ 1072-3374 ] ; 2008-04-01.
Abstract
Abstract: 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 R or C.
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DOI: 10.1007/s10958-008-0128-7
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