Local tube realizations of CR-manifolds and maximal abelian subalgebras
arXiv:0810.2019
Abstract
For every CR-manifold germ (M,a) local tube realizations are characterized by certain abelian subalgebras of the real Lie algebra hol(M,a) of all germs of (real-analytic) infinitesimal transformations. For instance, if M is holomorphically non-degenerate, every such subalgebra is maximal abelian and the classification of all local tube realizations for (M,a) reduces to a purely algebraic problem.
1 figure The text has been partly reorganized (especially sections 3 and 4) and simplified. Also extensions have been made such as in Lemma 3.1 (former Lemma 4.1) and for the examples in Section 4 (now for compact SU(p,q)-orbits in Grassmann spaces, formerly at the end of Section 3 only in projective spaces)