| dc.creator | Monera, M. G. | |
| dc.creator | Montesinos-Amilibia, A. | |
| dc.creator | Moraes, S. M. | |
| dc.creator | Sanabria-Codesal, E. | |
| dc.date | 2018-09-21T11:43:36Z | |
| dc.date | 2018-09-21T11:43:36Z | |
| dc.date | 2012-02-01 | |
| dc.date.accessioned | 2023-09-27T20:37:35Z | |
| dc.date.available | 2023-09-27T20:37:35Z | |
| dc.identifier | 01668641 | |
| dc.identifier | https://doi.org/10.1016/j.topol.2011.09.029 | |
| dc.identifier | http://www.locus.ufv.br/handle/123456789/21909 | |
| dc.identifier.uri | https://repositorioslatinoamericanos.uchile.cl/handle/2250/8945237 | |
| dc.description | We study the critical points of the normal map ν : N M → R k + n , where M is an immersed k-dimensional submanifold of R k + n , N M is the normal bundle of M and ν ( m , u ) = m + u if u ∈ N m M. Usually, the image of these critical points is called the focal set. However, in that set there is a subset where the focusing is highest, as happens in the case of curves in R 3 with the curve of the centers of spheres with contact of third order with the curve.
We give a definition of r-critical points of a smooth map between manifolds, and apply it to study the 2 and 3-critical points of the normal map in general and the 2-critical points for the case k = n = 2 in detail. In the later case we analyze the relation with the strong principal directions of Montaldi (1986) [2]. | |
| dc.format | pdf | |
| dc.format | application/pdf | |
| dc.language | eng | |
| dc.publisher | Topology and its Applications | |
| dc.relation | v. 159, n. 2, p. 537- 544, 1 fev. 2012 | |
| dc.rights | Open Access | |
| dc.subject | Normal map | |
| dc.subject | Critical points | |
| dc.subject | Focal set | |
| dc.subject | Strong principal directions | |
| dc.subject | Veronese of curvature | |
| dc.subject | Ellipse of curvature | |
| dc.title | Critical points of higher order for the normal map of immersions in R^ d | |
| dc.type | Artigo | |
