|
|||||
|
|
|
|
|
|
|
|
|
|
Singularities of flat
fronts in hyperbolic space
Masatoshi Kokubu, Wayne Rossman, Kentaro Saji, Masaaki Umehara and Kotaro Yamada |
|
Vol. 221 (2005), No. 2, 303–351
|
|
Correction: 10.2140/pjm.2018.294.505
|
Abstract |
|
It is well-known that the unit cotangent bundle of any Riemannian manifold has a canonical contact structure. A surface in a Riemannian 3-manifold is called a front if it is the projection of a Legendrian immersion into the unit cotangent bundle. We give easily computable criteria for a singular point on a front to be a cuspidal edge or a swallowtail. Using this, we prove that generically flat fronts in hyperbolic 3-space admit only cuspidal edges and swallowtails. We also show that any complete flat front (provided it is not rotationally symmetric) has associated parallel surfaces whose singularities consist of only cuspidal edges and swallowtails. |
Keywords
flat front, hyperbolic 3-space, cuspidal edge singularity,
swallowtail singularity
|
Mathematical Subject Classification 2000
Primary: 53C42
Secondary: 53A99
|
Milestones
Received: 27 December 2003
Revised: 23 March 2004
Accepted: 20 December 2004
Published: 1 October 2005
Correction: 20 February 2018
|
Authors |
| Masatoshi Kokubu | |
| Department of Natural Science School of Engineering Tokyo Denki University 2-2 Kanda-Nishiki-Cho Chiyoda-Ku, Tokyo 101-8457 Japan |
|
| Wayne Rossman | |
| Department of Mathematics Faculty of Science Kobe University Rokko, Kobe 657-8501 Japan |
|
| Kentaro Saji | |
| Department of Mathematics Hokkaido University Sapporo 060-0810 Japan |
|
| Masaaki Umehara | |
| Department of Mathematics Graduate School of Science Osaka University Toyonaka, Osaka 560-0043 Japan |
|
| Kotaro Yamada | |
| Faculty of Mathematics Kyushu University Higashi-Ku Fukuoka 812-8581 Japan |
|