LOCAL SYMPLECTIC INVARIANTS FOR CURVES
LOCAL SYMPLECTIC INVARIANTS FOR CURVES
复制标题
DOI：
10.1142/s0219199709003326
复制
发表时间：
2009-04
影响因子：
1.6
通讯作者：
N. Kamran;P. Olver;K. Tenenblat
中科院分区：
文献类型：
--
作者：
N. Kamran;P. Olver;K. Tenenblat
我们认为曲线在2n赋予标准的辛结构。本文引入曲线的辛弧长概念。我们构造了一个自适应的辛Frenet框架，我们定义了2n - 1个局部微分不变量，我们称之为曲线的辛曲率。我们证明了，直到一个刚性辛运动的<$2n，存在唯一的曲线与规定的辛曲率。我们用常辛曲率刻画了图4中的曲线。
We consider curves in ℝ2n endowed with the standard symplectic structure. We introduce the concept of symplectic arc length for curves. We construct an adapted symplectic Frenet frame and we define 2n - 1 local differential invariants that we call symplectic curvatures of the curve. We prove that up to a rigid symplectic motion of ℝ2n, there exists a unique curve with prescribed symplectic curvatures. We characterize the curves in ℝ4 with constant symplectic curvatures.