2023/04/29 by W. Barrera, Barrera, W., E. Montiel +3
Mathematics · #22E40 #51M10 #Advanced Algebra and Geometry #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2305.00153
openalex publication_date 2023/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider discrete subgroups of the group of orientation preserving isometries of the m-dimensional hyperbolic space, whose limit set is a (m-1)-dimensional real sphere, acting on the n-dimensional complex projective space for n≥ m, via an embedding from the group of orientation preserving isometries of the m-dimensional hyperbolic space to the group of holomorphic isometries of the n-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 n=m. In the other cases, we use some suitable projections of the the n-dimensional complex projective space to the m-dimensional complex projective space.