Metrics in the space of curves
| dc.creator | Yezzi, A. | |
| dc.creator | Mennucci, A. | |
| dc.date | 2004-12-22 | |
| dc.date | 2005-05-25 | |
| dc.date.accessioned | 2026-07-07T05:15:35Z | |
| dc.date.available | 2026-07-07T05:15:35Z | |
| dc.description | In this paper we study geometries on the manifold of curves. We define a manifold $M$ where objects $c\in M$ are curves, which we parameterize as $c:S^1\to \real^n$ ($n\ge 2$, $S^1$ is the circle). Given a curve $c$, we define the tangent space $T_cM$ of $M$ at $c$ including in it all deformations $h:S^1\to\real^n$ of $c$. We discuss Riemannian and Finsler metrics $F(c,h)$ on this manifold $M$, and in particular the case of the geometric $H^0$ metric $F(c,h)=\int |h|^2ds$ of normal deformations $h$ of $c$; we study the existence of minimal geodesics of $H^0$ under constraints; we moreover propose a conformal version of the $H^0$ metric. | |
| dc.description | 59 pages, 10 figures | |
| dc.identifier | https://arxiv.org/abs/math/0412454 | |
| dc.identifier | http://arxiv.org/abs/math/0412454 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73678 | |
| dc.subject | Differential Geometry | |
| dc.subject | Functional Analysis | |
| dc.subject | 58B20, 58D15, 58E10 | |
| dc.title | Metrics in the space of curves | |
| dc.type | text |