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

Stratmann, Bernd

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

Keywords:

symplectic manifold; real Lie group; symplectic reduction; complexification