Authors

Mohammad Shafiee

Abstract

In this paper we study some aspects of the relationship between cosymplectic and symplectic structures. In particular, we show that similar to the symplectic case, one can prove a nonsqueezing theorem for cosymplectomorphisms on R 2 m + 1 . Using this nonsqueezing theorem, we can define the concept of “cosymplectic capacity”. We show that the set of all cosymplectic capacities on cosymplectic manifolds of dimension 2 m + 1 has a close relationship with the set of all symplectic capacities on symplectic manifolds of dimension 2m. Furthermore, we study the relationship between fixed points of cosymplectomorphisms and symplectomorphisms.

Keywords

Symplectic structure; Cosymplectic structure; B-symplectic structure; Symplectic capacity; Cosymplectic capacity; Fixed point

Citation

BibTeX

@article{Shafiee_2022,
  title={{On the relation between cosymplectic and symplectic structures}},
  volume={178},
  ISSN={0393-0440},
  DOI={10.1016/j.geomphys.2022.104538},
  journal={Journal of Geometry and Physics},
  publisher={Elsevier BV},
  author={Shafiee, Mohammad},
  year={2022},
  pages={104538}
}

Download the bib file

References

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