Year: 2025
Type: preprint
Abstract: Given a quadratically convex compact connected oriented hypersurface $N$ of the complex hyperbolic plane, we prove that the characteristic rays of the symplectic form restricted to $N$ determine a double geodesic foliation of the exterior $U$ of $N$. This induces an outer billiard map $B$ on $U$. We prove that $B$ is a diffeomorphism (notice that weaker notions of strict convexity may allow the billiard map to be well-defined and invertible, but not smooth) and moreover, a symplectomorphism. These results generalize known geometric properties of the outer billiard maps in the hyperbolic plane and complex Euclidean space.
Source: arXiv (Cornell University)
Authors: Godoy, Yamile, Salvai, Marcos
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6979375704
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