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arXiv · 2608.22568

Distance preservers for Lobachevsky space

Alexander Belton·Dominique Guillot·Apoorva Khare·Mihai Putinar
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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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Alexander Belton, Dominique Guillot, Apoorva Khare, Mihai Putinar. 2026-09-22. Distance preservers for Lobachevsky space. https://arxiv.org/abs/2608.22568

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