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.
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