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

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].


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


Zbl 0287.57018