On Integrable Nets in General and Concordant Chebyshev Nets in Particular

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F25%3AA0000186" target="_blank" >RIV/47813059:19610/25:A0000186 - isvavai.cz</a>

Výsledek na webu

<a href="https://sigma-journal.com/2025/029/" target="_blank" >https://sigma-journal.com/2025/029/</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3842/SIGMA.2025.029" target="_blank" >10.3842/SIGMA.2025.029</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On Integrable Nets in General and Concordant Chebyshev Nets in Particular

Popis výsledku v původním jazyce

We consider general integrable curve nets in Euclidean space as a particular integrable geometry invariant with respect to rigid motions and net-preserving reparameterisations. For the purpose of their description, we first give an overview of the most important second-order invariants and relations among them. As a particular integrable example, we reinterpret the result of I.S. Krasil'shchik and M. Marvan (see Section 2, Case 2 in [Acta Appl. Math. 56 (1999), 217-230]) as a curve net satisfying an ℝ -linear relation between the Schief curvature of the net and the Gauss curvature of the supporting surface. In the special case when the curvatures are proportional (concordant nets), we find a correspondence to pairs of pseudospherical surfaces of equal negative constant Gaussian curvatures. Conversely, we also show that two generic pseudospherical surfaces of equal negative constant Gaussian curvatures induce a concordant Chebyshev net. The construction generalises the well-known correspondence between pairs of curves and translation surfaces.

Název v anglickém jazyce

On Integrable Nets in General and Concordant Chebyshev Nets in Particular

Popis výsledku anglicky

We consider general integrable curve nets in Euclidean space as a particular integrable geometry invariant with respect to rigid motions and net-preserving reparameterisations. For the purpose of their description, we first give an overview of the most important second-order invariants and relations among them. As a particular integrable example, we reinterpret the result of I.S. Krasil'shchik and M. Marvan (see Section 2, Case 2 in [Acta Appl. Math. 56 (1999), 217-230]) as a curve net satisfying an ℝ -linear relation between the Schief curvature of the net and the Gauss curvature of the supporting surface. In the special case when the curvatures are proportional (concordant nets), we find a correspondence to pairs of pseudospherical surfaces of equal negative constant Gaussian curvatures. Conversely, we also show that two generic pseudospherical surfaces of equal negative constant Gaussian curvatures induce a concordant Chebyshev net. The construction generalises the well-known correspondence between pairs of curves and translation surfaces.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2025

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Symmetry, Integrability and Geometry: Methods and Applications

ISSN

1815-0659

e-ISSN

—

Svazek periodika

21

Číslo periodika v rámci svazku

April

Stát vydavatele periodika

UA - Ukrajina

Počet stran výsledku

34

Strana od-do

„029-1“-„029-34“

Kód UT WoS článku

001478828100001

EID výsledku v databázi Scopus

2-s2.0-105005534439