preprint draft Martin Bauer author Sadashige Ishida author 6F7C4B96-A8E9-11E9-A7CA-09ECE56974250000-0002-3121-3100 Peter W. Michor author GradSch department ChWo department Computational Discovery of Numerical Algorithms for Animation and Simulation of Natural Phenomena project 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. 2024 eng space of space curvessymplectic stuctures 2407.1990810.48550/arXiv.2407.19908 https://research-explorer.ista.ac.at/record/20551 Bauer, Martin, et al. “Symplectic Structures on the Space of Space Curves.” <i>ArXiv</i>, doi:<a href="https://doi.org/10.48550/arXiv.2407.19908">10.48550/arXiv.2407.19908</a>. Bauer M, Ishida S, Michor PW. Symplectic structures on the space of space curves. arXiv, <a href="https://doi.org/10.48550/arXiv.2407.19908">10.48550/arXiv.2407.19908</a>. M. Bauer, S. Ishida, P.W. Michor, ArXiv (n.d.). M. Bauer, S. Ishida, and P. W. Michor, “Symplectic structures on the space of space curves,” <i>arXiv</i>. . Bauer, M., Ishida, S., &#38; Michor, P. W. (n.d.). Symplectic structures on the space of space curves. <i>arXiv</i>. <a href="https://doi.org/10.48550/arXiv.2407.19908">https://doi.org/10.48550/arXiv.2407.19908</a> Bauer, Martin, Sadashige Ishida, and Peter W. Michor. “Symplectic Structures on the Space of Space Curves.” <i>ArXiv</i>, n.d. <a href="https://doi.org/10.48550/arXiv.2407.19908">https://doi.org/10.48550/arXiv.2407.19908</a>. Bauer M, Ishida S, Michor PW. Symplectic structures on the space of space curves. <i>arXiv</i>. doi:<a href="https://doi.org/10.48550/arXiv.2407.19908">10.48550/arXiv.2407.19908</a> 173612024-08-01T06:34:08Z2026-04-07T12:02:23Z