## Complexification of proper Hamiltonian $$G$$-spaces.(English)Zbl 0915.32003

Schriftenreihe des Graduiertenkollegs Geometrie und Mathematische Physik. 29. Bochum: Univ. Bochum, Institut für Mathematik, 29 p. (1998).
From the introduction: “Let $$(M,\tau)$$ be a symplectic manifold and $$G$$ a real Lie group acting properly by symplectic automorphisms on $$(M,\tau)$$.
The goal of this paper is to complexify $$(M, \tau,G)$$. This is of interest since the symplectic reduction of a complex manifold is itself a complex space. This provides a method for analyzing the symplectic reduction of $$M$$ via its embedding in the symplectic reduction of the complexification of $$M$$”.

### MSC:

 32E10 Stein spaces 53C10 $$G$$-structures 32Q15 Kähler manifolds 32-02 Research exposition (monographs, survey articles) pertaining to several complex variables and analytic spaces