---
OA_place: repository
_id: '17361'
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.
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.
article_processing_charge: No
arxiv: 1
author:
- first_name: Martin
  full_name: Bauer, Martin
  last_name: Bauer
- first_name: Sadashige
  full_name: Ishida, Sadashige
  id: 6F7C4B96-A8E9-11E9-A7CA-09ECE5697425
  last_name: Ishida
  orcid: 0000-0002-3121-3100
- first_name: Peter W.
  full_name: Michor, Peter W.
  last_name: Michor
citation:
  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>
  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>
  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>.
  ieee: M. Bauer, S. Ishida, and P. W. Michor, “Symplectic structures on the space
    of space curves,” <i>arXiv</i>. .
  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>.
  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.).
date_created: 2024-08-01T06:34:08Z
date_published: 2024-07-29T00:00:00Z
date_updated: 2026-04-07T12:02:23Z
day: '29'
department:
- _id: GradSch
- _id: ChWo
doi: 10.48550/arXiv.2407.19908
external_id:
  arxiv:
  - '2407.19908'
keyword:
- space of space curves
- symplectic stuctures
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2407.19908
month: '07'
oa: 1
oa_version: Preprint
project:
- _id: 34bc2376-11ca-11ed-8bc3-9a3b3961a088
  grant_number: '101045083'
  name: Computational Discovery of Numerical Algorithms for Animation and Simulation
    of Natural Phenomena
publication: arXiv
publication_status: draft
related_material:
  record:
  - id: '20551'
    relation: dissertation_contains
    status: public
status: public
title: Symplectic structures on the space of space curves
type: preprint
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
year: '2024'
...