Symplectic Structures on the Space of Space Curves
Abstract
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. Supplementary Information: The online version contains supplementary material available at 10.1007/s00332-026-10266-8.
Fields of Study & Subjects
Geometric and Algebraic Topology
Geometry and complex manifolds
Geometric Analysis and Curvature Flows
Publication details
- Journal / source
- Journal of Nonlinear Science
- Publisher
- Springer Science and Business Media LLC
- Volume
- 36
- Issue
- 2
- Pages
- 45–45
- Publication date
- 1 April 2026
- Language
- EN