PreprintCC BY 4.0arXiv
Geodesic simplices of pseudo-hyperbolic space
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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BibTeX
@misc{lemistre2026geodesic,
title = {{Geodesic simplices of pseudo-hyperbolic space}},
author = {Timothé Lemistre},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2605.06254},
eprint = {2605.06254},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.06254},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Geodesic simplices of pseudo-hyperbolic space
AU - Timothé Lemistre
PY - 2026
DA - 2026/08/30
PB - arXiv
DO - 10.48550/arxiv.2605.06254
UR - https://arxiv.org/abs/2605.06254
AB - 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.
ER -