No CrossRef data available.
Article contents
On the group of automorphisms of the Euclidean hypersphere
Published online by Cambridge University Press: 26 February 2010
Extract
Let Cn be the n-dimensional complex number space of the complex variables z1,…, zn and 
be the unit hypersphere. Further, let G be the group of all holomorphic automorphisms of K, then G is a n(n + 2)-dimensional real Lie group. In [3] the author has proved that for any P∈∂K (the boundary of K) there exists a decomposition of G in the form 
, where G0 is the group of all analytic rotations about the origin and 
is a 2n-dimensional real Lie group, whose underlying topological space is K, which acts transitively on K and P is a fixed point of all elements of .
- Type
- Research Article
- Information
- Copyright
- Copyright © University College London 1968
References
1.Behnke, und Thullen, , Theorie der Funktionen mehrerer Komplexer Veränderlichen, Erg. Math., 3 (Berlin, 1934).Google Scholar
2.Fadlalla, A. A., “The Carathéodory limiting spherical shells in the Euclidean hypersphere”, Mathematika, 13 (1966), 69–75.CrossRefGoogle Scholar
3.Fadlalla, A. A. “On the group of automorphisms of the Euclidean hypersphere”, Quart. J. Math., Oxford (2), 18 (1967), 97–101.CrossRefGoogle Scholar
5.Sperner, E., Einfiihrung in die analytische Geometrie und Algebra, 2 Teil, 3 aufl (Göottingen, 1959).Google Scholar