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Complex hyperbolic surfaces whose closed geodesics are all simple
Sami Douba, D. B. McReynolds, Julien Paupert, Jonathan Vittore
Source abstract
We show that all closed geodesics in any arithmetic complex hyperbolic surface of second type are simple. These include the fake projective planes studied by Mumford, Klingler, Prasad-Yeung, and Cartwright-Steger.
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