An elementary proof of Small's formula for null curves in PSL(2,C) and an analogue for Legendrian curves in PSL(2,C)
| dc.creator | Kokubu, Masatoshi | |
| dc.creator | Umehara, Masaaki | |
| dc.creator | Yamada, Kotaro | |
| dc.date | 2002-09-20 | |
| dc.date | 2003-02-21 | |
| dc.date.accessioned | 2026-07-07T04:51:04Z | |
| dc.date.available | 2026-07-07T04:51:04Z | |
| dc.description | For null curves in PSL(2,C), there exists a representation formula in terms of two meromorphic functions and their derivatives (Small's formula). In this paper, we give an elementary proof of Small's formula. Moreover, a similar formula for Legendrian curves in PSL(2,C) is given. As null curves in PSL(2,C) are related to mean curvature one surfaces in hyperbolic 3-space H^3, Legendrian curves are related to flat surfaces in H^3. So, as an application of Small-type formula for Lengendrian curves, we give new examples of flat surfaces in H^3. | |
| dc.description | 13 pages, 9 figures | |
| dc.identifier | https://arxiv.org/abs/math/0209258 | |
| dc.identifier | http://arxiv.org/abs/math/0209258 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65012 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53A10; 53A35; 53A07 | |
| dc.title | An elementary proof of Small's formula for null curves in PSL(2,C) and an analogue for Legendrian curves in PSL(2,C) | |
| dc.type | text |