Geodesic simplices of pseudo-hyperbolic space

Timothé Lemistre

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arXiv · 2605.06254

Geodesic simplices of pseudo-hyperbolic space

Timothé Lemistre

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Abstract

We give a cohomological interpretation of the geodesic simplices of the pseudo-hyperbolic space of signature $(p,q)$ and formulate a necessary and sufficient condition for such a simplex to have finite volume. As a corollary, we obtain that every ideal geodesic polytope in the pseudo-hyperbolic space of signature $(2,2)$ has finite volume.

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Timothé Lemistre. 2026-05-07. Geodesic simplices of pseudo-hyperbolic space. https://arxiv.org/abs/2605.06254

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