The Amsler Surface: Complete Theory and Numerical Implementation

This comprehensive document presents the complete mathematical theory of the Amsler surface — a classical pseudospherical surface of constant negative curvature K = −1 — for the general case where the initial angle ω0 between the straight asymptotic lines is arbitrary. We provide a complete derivation of the differential equations, including the correct initial conditions. Last version is available at https://zenodo.org/records/18253019

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-01-13
DOI
https://doi.org/10.5281/zenodo.18230229
Primary Topic
Geometric Analysis and Curvature Flows
Type
article
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article

The Amsler Surface: Complete Theory and Numerical Implementation

A Kalmykov
Zenodo (CERN European Organization for Nuclear Research)
Geometric Analysis and Curvature Flows
article

The Amsler Surface: Complete Theory and Numerical Implementation

A Kalmykov
article en

Abstract

This comprehensive document presents the complete mathematical theory of the Amsler surface — a classical pseudospherical surface of constant negative curvature K = −1 — for the general case where the initial angle ω0 between the straight asymptotic lines is arbitrary. We provide a complete derivation of the differential equations, including the correct initial conditions. Last version is available at https://zenodo.org/records/18253019

Zenodo (CERN European Organization for Nuclear Research)
Openalex Percentile: Top 88%
Geometric Analysis and Curvature Flows
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The Amsler Surface: Complete Theory and Numerical Implementation — A Kalmykov · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS