Examples of Unbounded Homogeneous Domains in Complex Space
Abstract
We construct several new examples of homogeneous domains in complex space that do not have bounded realisations. They are equivalent to tubes over affinely homogeneous domains in real space and have a real-analytic everywhere Levi non-degenerate non-umbilic boundary. Using the geometry of the boundary, we determine the full automorphism groups of the domains. We also discuss some interesting examples of tube domains with everywhere umbilic boundary (i.e., boundary equivalent to the corresponding quadric).
Cite
@article{arxiv.math/0304102,
title = {Examples of Unbounded Homogeneous Domains in Complex Space},
author = {Michael Eastwood and Alexander Isaev},
journal= {arXiv preprint arXiv:math/0304102},
year = {2007}
}
Comments
Since writing this article, the authors have discovered that the homogeneous domains presented therein are already analysed by Richard Penney in "Homogeneous Koszul manifolds in C^n", Jour. Diff. Geom. 36 (1992) 591--631, where they occur as the Example on page 629. The new aspect is the manner in which these domains arise, namely as tubes over an affine homogeneous base