Vortices on closed surfaces

Details Vortices on closed surfaces Vortices on closed surfaces

2008-02-29

arxiv.org/abs/0802.4313v1

Mathematics

Symplectic Geometry

Scientific paper

We consider $N$ point vortices $s_j$ of strengths $\kappa_j$ moving on a closed (compact, boundaryless, orientable) surface $S$ with riemannian metric $g$. As far as we know, only the sphere or surfaces of revolution, the latter qualitatively, have been treated in the available literature. The aim of this note is to present an intrinsic geometric formulation for the general case. We give a simple proof of Kimura's conjecture that a dipole describes geodesic motion. Searching for integrable vortex pairs systems on Liouville surfaces is in order. The vortex pair system on a triaxial ellipsoid extends Jacobi's geodesics. Is it Arnold-Liouville integrable? Not in our wildest dreams is another possibility: that quantizing a vortex system could relate with a million dollars worth question, but we took courage - nerve is more like it - to also present it.

Affiliated with

Also associated with

No associations

Rating

Vortices on closed surfaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Vortices on closed surfaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Vortices on closed surfaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-352292