{"doi":"10.48550/arXiv.2407.19908","author":[{"first_name":"Martin","full_name":"Bauer, Martin","last_name":"Bauer"},{"last_name":"Ishida","id":"6F7C4B96-A8E9-11E9-A7CA-09ECE5697425","full_name":"Ishida, Sadashige","first_name":"Sadashige"},{"last_name":"Michor","full_name":"Michor, Peter W.","first_name":"Peter W."}],"external_id":{"arxiv":["2407.19908"]},"day":"29","_id":"17361","oa_version":"Preprint","publication":"arXiv","year":"2024","abstract":[{"lang":"eng","text":"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."}],"project":[{"grant_number":"101045083","name":"Computational Discovery of Numerical Algorithms for Animation and Simulation of Natural Phenomena","_id":"34bc2376-11ca-11ed-8bc3-9a3b3961a088"}],"date_created":"2024-08-01T06:34:08Z","language":[{"iso":"eng"}],"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.","month":"07","citation":{"mla":"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>.","short":"M. Bauer, S. Ishida, P.W. Michor, ArXiv (n.d.).","ista":"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>.","chicago":"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>.","ama":"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>","ieee":"M. Bauer, S. Ishida, and P. W. Michor, “Symplectic structures on the space of space curves,” <i>arXiv</i>. .","apa":"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>"},"date_published":"2024-07-29T00:00:00Z","date_updated":"2024-08-01T08:20:29Z","keyword":["space of space curves","symplectic stuctures"],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2407.19908"}],"article_processing_charge":"No","title":"Symplectic structures on the space of space curves","oa":1,"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","type":"preprint","publication_status":"submitted","department":[{"_id":"GradSch"},{"_id":"ChWo"}],"status":"public"}