Action of $\mathbb{R}$-Fuchsian groups on $\mathbb{P}_\mathbb{C}^n$
Abstract
We consider discrete subgroups of the group of orientation preserving isometries of the -dimensional hyperbolic space, whose limit set is a -dimensional real sphere, acting on the -dimensional complex projective space for , via an embedding from the group of orientation preserving isometries of the -dimensional hyperbolic space to the group of holomorphic isometries of the -dimensional complex hyperbolic space. We describe the Kulkarni limit set of any of these subgroups under the embedding as a real semi-algebraic set. Also, we show that the Kulkarni region of discontinuity can only have one or three connected components. We use the Sylvester's law of inertia when . In the other cases, we use some suitable projections of the the -dimensional complex projective space to the -dimensional complex projective space.
Cite
@article{arxiv.2305.00153,
title = {Action of $\mathbb{R}$-Fuchsian groups on $\mathbb{P}_\mathbb{C}^n$},
author = {W. Barrera and E. Montiel and J. P. Navarrete},
journal= {arXiv preprint arXiv:2305.00153},
year = {2023}
}