Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2406.05971 |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
Sommario:
- This is a continuation of the authors' earlier work on deformations of cuspidal edges. We give a representation formula for swallowtails in the Euclidean 3-space. Using this, we investigate map germs of generic swallowtails in 3-dimensional space from, and show some important properties of them. In particular, we give a representation formula giving all map germs of swallowtails in the Euclidean 3-space whose Gaussian curvatures are bounded from below by a positive constant or by a negative constant from above. Using this, we show that any swallowtails are deformed into a swallowtail of constant Gaussian curvature preserving the sign of their Gaussian curvatures.