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<p>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.</p>

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Symplectic Structures on the Space of Space Curves

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年4月15日

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  • Martin Bauer,
  • Sadashige Ishida,
  • Peter W. Michor

摘要

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.