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.