This paper which is made up of seven theorems, eight lemmas and propositions, nine remarks, eleven examples, two corollaries and one question deals with various properties of the momentum map associated with the Hamiltonian actions of the compact Lie group \(U\) on a Kählerian manifold \(M\) and the real form \(G\) of its complexification \(U^{\mathbb C}\). It is claimed that when \(G\) is a compatible Lie subgroup of \(U^{\mathbb C}\) one can get a lot of information about the \(G\)-action on \(M\).
Details and complete proofs of various theorems, lemmas and propositions can be found in [P. Heinzner and G. Schwarz, Math. Ann. 337, No. 1, 197–232 (2007; Zbl 1110.32008)] and [P. Heinzner and H. Stötzel, Math. Ann. 338, No. 1, 1–9 (2007; Zbl 1129.32015)].
For the entire collection see [Zbl 1099.14001].