Symplectic structures on the space of space curves
Bauer M, Ishida S, Michor PW. 2026. Symplectic structures on the space of space curves. Journal of Nonlinear Science. 36(2), 45.
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Author
Bauer, Martin;
Ishida, SadashigeISTA 
;
Michor, Peter W.
;
Michor, Peter W.Department
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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.
Publishing Year
Date Published
2026-04-15
Journal Title
Journal of Nonlinear Science
Publisher
Springer Nature
Acknowledgement
The authors are grateful to Boris Khesin for valuable comments on the MW symplectic structure and S. Ishida thanks Albert Chern for insightful discussions on space curves and Chris Wojtan for his continuous support. M. Bauer was partially supported by NSF grant DMS-1953244 and by the Binational Science Foundation (BSF). S. Ishida was partially supported by ERC Consolidator Grant 101045083 “CoDiNA” funded by the European Research Council. Some figures were generated by the software Houdini and its education license was provided by SideFX. Open access funding provided by University of Vienna.
Volume
36
Issue
2
Article Number
45
ISSN
eISSN
IST-REx-ID
Cite this
Bauer M, Ishida S, Michor PW. Symplectic structures on the space of space curves. Journal of Nonlinear Science. 2026;36(2). doi:10.1007/s00332-026-10266-8
Bauer, M., Ishida, S., & Michor, P. W. (2026). Symplectic structures on the space of space curves. Journal of Nonlinear Science. Springer Nature. https://doi.org/10.1007/s00332-026-10266-8
Bauer, Martin, Sadashige Ishida, and Peter W. Michor. “Symplectic Structures on the Space of Space Curves.” Journal of Nonlinear Science. Springer Nature, 2026. https://doi.org/10.1007/s00332-026-10266-8.
M. Bauer, S. Ishida, and P. W. Michor, “Symplectic structures on the space of space curves,” Journal of Nonlinear Science, vol. 36, no. 2. Springer Nature, 2026.
Bauer M, Ishida S, Michor PW. 2026. Symplectic structures on the space of space curves. Journal of Nonlinear Science. 36(2), 45.
Bauer, Martin, et al. “Symplectic Structures on the Space of Space Curves.” Journal of Nonlinear Science, vol. 36, no. 2, 45, Springer Nature, 2026, doi:10.1007/s00332-026-10266-8.
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