RIEMANNIAN GEOMETRICAL ANALYSIS OF THE MOTION OF A VORTEX FILAMENT - A SYSTEM OF C-INFINITY(S-1, SO(3))

Citation
K. Suzuki et al., RIEMANNIAN GEOMETRICAL ANALYSIS OF THE MOTION OF A VORTEX FILAMENT - A SYSTEM OF C-INFINITY(S-1, SO(3)), Physical review letters, 77(9), 1996, pp. 1679-1682
Citations number
21
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Physics
Journal title
ISSN journal
0031-9007
Volume
77
Issue
9
Year of publication
1996
Pages
1679 - 1682
Database
ISI
SICI code
0031-9007(1996)77:9<1679:RGAOTM>2.0.ZU;2-2
Abstract
The motion of an isolated vortex filament with small curvature is gove rned by the local induction equation. The present work is an attempt t o study such an integrable system based on the Riemannian geometry of the solution manifold, by reformulating the governing equation as the geodesic equation on an infinite dimensional Lie group C-infinity(S-1, SO(3)). The sectional curvatures for the vector fields along the geode sic curves and their perturbations are calculated to show their tenden cy to be positive for some typical filaments such as a straight vortex , a helical vortex, and a vortex soliton.