Geometric structures on loop and path spaces
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- January 2008
- DOI:
- 10.48550/arXiv.0801.3545
- arXiv:
- arXiv:0801.3545
- Bibcode:
- 2008arXiv0801.3545M
- Keywords:
-
- Mathematics - Symplectic Geometry;
- Mathematics - Differential Geometry;
- 53D35;
- 55P35
- E-Print:
- Final version. To appear in Proceedings of Math. Sci. Indian Academy of Sciences