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Distance preservers for Lobachevsky space
Abstract
We obtain a complete description of the class of entrywise preservers of Lorentz-Gram matrices. This resolves, for the case of constant negative curvature, the classification of entrywise preservers obtained by Schoenberg in the zero-curvature (Euclidean) and constant-positive-curvature (spherical) settings. These preservers admit a Lévy--Khintchine-type representation and their asymptotic characteristics are related to Krein's classification of screw lines in Lobachevsky space. Connections with complete Nevanlinna--Pick kernels and Bochner subordination are also obtained.
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BibTeX
@misc{belton2026distance,
title = {{Distance preservers for Lobachevsky space}},
author = {Alexander Belton and Dominique Guillot and Apoorva Khare and Mihai Putinar},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.22568},
eprint = {2608.22568},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.22568},
}
RIS
TY - UNPB
TI - Distance preservers for Lobachevsky space
AU - Alexander Belton
AU - Dominique Guillot
AU - Apoorva Khare
AU - Mihai Putinar
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2608.22568
UR - https://arxiv.org/abs/2608.22568
AB - We obtain a complete description of the class of entrywise preservers of Lorentz-Gram matrices. This resolves, for the case of constant negative curvature, the classification of entrywise preservers obtained by Schoenberg in the zero-curvature (Euclidean) and constant-positive-curvature (spherical) settings. These preservers admit a Lévy--Khintchine-type representation and their asymptotic characteristics are related to Krein's classification of screw lines in Lobachevsky space. Connections with complete Nevanlinna--Pick kernels and Bochner subordination are also obtained.
ER -