A real analytic version of Abel’s theorem and complexifications of proper Lie group actions. (English) Zbl 0861.32011

Heinzner, Peter; Huckleberry, Alan T.; Kutzschebauch, Frank

Ancona, Vincenzo (ed.) et al., Complex analysis and geometry. Proceedings of the conference held in Trento, Italy, June 5-9, 1995. New York, NY: Marcel Dekker. Lect. Notes Pure Appl. Math. 173, 229-273 (1996).

The authors prove the following real analytic version of a result of H. Abels [Math. Ann. 212, 1-19 (1974; Zbl 0287.57018)] in the case of smooth actions: ‘Let \(M\) be a real analytic manifold and \(G\times M\to M\) be a proper real analytic action of a Lie group \(G\) which has finitely many components. Then there exist a \(G\)-equivariant real analytic map \(\pi: M\to G/K\), \(K\) denoting a maximal compact subgroup of \(G\).’
By complexifying the fiber and base of a real analytic Abels fibration they also construct a complexification of a proper action.
For the entire collection see [Zbl 0834.00039].

Reviewer: S.K.Chatterjea (Calcutta)

MSC:

32V40	Real submanifolds in complex manifolds
32C05	Real-analytic manifolds, real-analytic spaces

Keywords:

proper real analytic action of a Lie group; complexification

Citations:

Zbl 0287.57018