Abstract
We study oriented right-angled polygons in hyperbolic spaces of arbitrary dimensions, that is, finite sequences \(( S_0,S_1,\ldots ,S_{p-1})\) of oriented geodesics in the hyperbolic space \(\varvec{H}^{n+2}\) such that consecutive sides are orthogonal. It was previously shown by Delgove and Retailleau (Ann Fac Sci Toulouse Math 23(5):1049–1061, 2014. https://doi.org/10.5802/afst.1435) that three quaternionic parameters define a right-angled hexagon in the 5-dimensional hyperbolic space. We generalise this method to right-angled polygons with an arbitrary number of sides \(p\ge 5\) in a hyperbolic space of arbitrary dimension.
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Both authors would like to thank their Ph.D. supervisor Prof. Ruth Kellerhals for her encouragement and valuable advice throughout the work on this paper and for her constant support.
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Edoardo Dotti was partially supported by the Schweizerischer Nationalfonds 200020-156104.
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Dotti, E., Drewitz, S.T. On right-angled polygons in hyperbolic space. Geom Dedicata 200, 45–59 (2019). https://doi.org/10.1007/s10711-018-0357-y
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DOI: https://doi.org/10.1007/s10711-018-0357-y