English

Geometric structures on loop and path spaces

Symplectic Geometry 2010-09-16 v2 Differential Geometry

Abstract

Is is known that the loop space associated to a Riemannian manifold admits a quasi-symplectic structure. This article shows that this structure is not likely to recover the underlying Riemannian metric by proving a result that is a strong indication of the "almost" independence of the quasi-symplectic structure with respect to the metric. Finally conditions to have contact structures on these spaces are studied.

Keywords

Cite

@article{arxiv.0801.3545,
  title  = {Geometric structures on loop and path spaces},
  author = {Vicente Munoz and Francisco Presas},
  journal= {arXiv preprint arXiv:0801.3545},
  year   = {2010}
}

Comments

Final version. To appear in Proceedings of Math. Sci. Indian Academy of Sciences

R2 v1 2026-06-21T10:05:37.940Z