Additional first order equation for infinitesimal bendings of smooth surfaces in the isothermal coordinates Full article
| Journal |
Siberian Mathematical Journal
ISSN: 0037-4466 , E-ISSN: 1573-9260 |
||||
|---|---|---|---|---|---|
| Output data | Year: 2025, Volume: 66, Number: 3, Pages: 618-628 Pages count : 11 DOI: 10.1134/S0037446625030024 | ||||
| Tags | Euclidean 3-space, surface in Euclidean space, infinitesimal bending of a surface, Darboux rotation field, isothermal coordinates, elliptic partial differential equation, maximum principle | ||||
| Authors |
|
||||
| Affiliations |
|
Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0006 |
Abstract:
The article contributes to the theory of infinitesimal bendings of smooth surfaces in Euclidean 3-space. We derive a certain linear differential equation of the first order, which previously did not appear in the literature and which is satisfied by any Darboux rotation field of a smooth surface. We show that, for some surfaces, this additional equation is functionally independent of the three standard equations that the Darboux rotation field satisfies (and by which it is determined). As a consequence of this additional equation, we prove the maximum principle for the components of the Darboux rotation field for disk-homeomorphic surfaces with strictly positive Gaussian curvature.
Cite:
Alexandrov V.A.
Additional first order equation for infinitesimal bendings of smooth surfaces in the isothermal coordinates
Siberian Mathematical Journal. 2025. V.66. N3. P.618-628. DOI: 10.1134/S0037446625030024 Scopus РИНЦ OpenAlex
Additional first order equation for infinitesimal bendings of smooth surfaces in the isothermal coordinates
Siberian Mathematical Journal. 2025. V.66. N3. P.618-628. DOI: 10.1134/S0037446625030024 Scopus РИНЦ OpenAlex
Original:
Александров В.А.
Дополнительное уравнение первого порядка для бесконечно малых изгибаний гладких поверхностей в изотермических координатах
Сибирский математический журнал. 2025. Т.66. №3. С.349-362. DOI: 10.33048/smzh.2025.66.302
Дополнительное уравнение первого порядка для бесконечно малых изгибаний гладких поверхностей в изотермических координатах
Сибирский математический журнал. 2025. Т.66. №3. С.349-362. DOI: 10.33048/smzh.2025.66.302
Dates:
| Submitted: | Oct 18, 2024 |
| Accepted: | Apr 25, 2025 |
| Published print: | Jun 2, 2025 |
| Published online: | Jun 2, 2025 |
Identifiers:
| Scopus: | 2-s2.0-105007138298 |
| Elibrary: | 82395828 |
| OpenAlex: | W4410947259 |
Citing:
Пока нет цитирований