Poisson geometry of differential invariants of curves in some nonsemisimple homogeneous spaces

被引：33

作者：

Beffa, GM ^{[1
]}

机构：

[1] Univ Wisconsin, Dept Math, Madison, WI 53706 USA

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2006年 / 134卷 / 03期

关键词：

invariant evolutions of curves; homogeneous spaces; infinite dimensional Poisson geometry; differential invariants; completely integrable PDEs;

D O I：

10.1090/S0002-9939-05-07998-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we describe a family of compatible Poisson structures defined on the space of coframes (or differential invariants) of curves in. at homogeneous spaces of the form M congruent to (G x R-n)/G where G subset of GL(n, R) is semisimple. This includes Euclidean, affine, special affine, Lorentz, and symplectic geometries. We also give conditions on geometric evolutions of curves in the manifold M so that the induced evolution on their differential invariants is Hamiltonian with respect to our main Hamiltonian bracket.

引用

页码：779 / 791

页数：13