空间曲线空间的交映结构

arXiv - MATH - Symplectic Geometry Pub Date : 2024-07-29 DOI:arxiv-2407.19908

Martin Bauer, Sadashige Ishida, Peter W. Michor

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引用次数: 0

摘要

我们提出了无参数化空间曲线形状空间上的交映结构，它概括了经典的马斯登-韦恩斯坦结构。我们的方法将马斯登-韦恩斯坦结构的柳维尔 1-form 与数学形状分析中引入的黎曼结构整合在一起。我们还推导了关于这些新交映结构的几个经典哈密顿函数的哈密顿向量场。

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Symplectic structures on the space of space curves

We present symplectic structures on the shape space of unparameterized space curves that generalize the classical Marsden-Weinstein structure. Our method integrates the Liouville 1-form of the Marsden-Weinstein structure with Riemannian structures that have been introduced in mathematical shape analysis. We also derive Hamiltonian vector fields for several classical Hamiltonian functions with respect to these new symplectic structures.

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arXiv - MATH - Symplectic Geometry

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