On Integrable Nets in General and Concordant Chebyshev Nets in Particular
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
On Integrable Nets in General and Concordant Chebyshev Nets in Particular
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Symmetry, Integrability and Geometry: Methods and Applications
ISSN
1815-0659
e-ISSN
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Volume of the periodical
21
Issue of the periodical within the volume
April
Country of publishing house
UA - UKRAINE
Number of pages
34
Pages from-to
„029-1“-„029-34“
UT code for WoS article
001478828100001
EID of the result in the Scopus database
2-s2.0-105005534439