Behavior of corank one singular points on wave fronts
| dc.creator | Saji, Kentaro | |
| dc.creator | Umehara, Masaaki | |
| dc.creator | Yamada, Kotaro | |
| dc.date | 2007-04-21 | |
| dc.date | 2007-05-18 | |
| dc.date.accessioned | 2026-07-07T08:01:56Z | |
| dc.date.available | 2026-07-07T08:01:56Z | |
| dc.description | Let $M^2$ be an oriented 2-manifold and $f:M^2\to R^3$ a $C^\infty$-map. A point $p\in M^2$ is called a singular point if $f$ is not an immersion at $p$. The map $f$ is called a front (or wave front), if there exists a unit $C^\infty$-vector field $ν$ such that the image of each tangent vector $df(X)$ $(X\in TM^2)$ is perpendicular to $ν$, and the pair $(f,ν)$ gives an immersion into $R^3\times S^2$. In our previous paper, we gave an intrinsic formulation of wave fronts in $R^3$. In this paper, we shall investigate the behavior of cuspidal edges near corank one singular points and establish Gauss-Bonnet-type formulas under the intrinsic formulation. | |
| dc.description | 20 pages, 12 figures | |
| dc.identifier | https://arxiv.org/abs/0704.2810 | |
| dc.identifier | http://arxiv.org/abs/0704.2810 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/129075 | |
| dc.subject | Differential Geometry | |
| dc.subject | 57R45; 53A05 | |
| dc.title | Behavior of corank one singular points on wave fronts | |
| dc.type | text |