Locally homogeneous finitely nondegenerate CR-manifolds
Complex Variables
2007-05-23 v1 Group Theory
Abstract
Germs of locally homogeneous CR manifolds M can be characterized in terms of certain algebraic data, e.g., by CR-algebras. We give an explicit formula which relates the Levi form of such an M and its higher order analogues to the Lie brackets in certain finite dimensional Lie algebras. As an application we give a simple characterization of geometric properties of M such as minimality, k-nondegeneracy, holomorphic degeneracy etc. in purely algebraic terms. We present an example of a homogeneous 3-nondegenerate CR-manifold. We also determine a universal upper bound for the order k of k-nondegenerate orbits of real forms in flag manifolds.
Keywords
Cite
@article{arxiv.math/0606032,
title = {Locally homogeneous finitely nondegenerate CR-manifolds},
author = {Gregor Fels},
journal= {arXiv preprint arXiv:math/0606032},
year = {2007}
}