Additional first order equation for infinitesimal bendings of smooth surfaces in the isothermal coordinates
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909637887918080 |
|---|---|
| author | Alexandrov, Victor |
| author_facet | Alexandrov, Victor |
| contents | The article contributes to the theory of infinitesimal bendings of smooth surfaces in Euclidean 3-space. We derive a 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 a class of disk-homeomorphic surfaces containing not only surfaces of positive Gaussian curvature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_13634 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Additional first order equation for infinitesimal bendings of smooth surfaces in the isothermal coordinates Alexandrov, Victor Differential Geometry 53C24, 53A05, 53C18, 52C25 The article contributes to the theory of infinitesimal bendings of smooth surfaces in Euclidean 3-space. We derive a 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 a class of disk-homeomorphic surfaces containing not only surfaces of positive Gaussian curvature. |
| title | Additional first order equation for infinitesimal bendings of smooth surfaces in the isothermal coordinates |
| topic | Differential Geometry 53C24, 53A05, 53C18, 52C25 |
| url | https://arxiv.org/abs/2410.13634 |