Geometric structures on loop and path spaces

2008/01/23 by Vicente Munoz, Francisco Presas, Munoz, Vicente +1
Mathematics · #53D35 #55P35 #Differential Geometry (math.DG) #FOS: Mathematics #Symplectic Geometry (math.SG) #math.DG #math.SG #msc:53D35 #msc:55P35

paper · pdf · doi:10.48550/arxiv.0801.3545

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

arxiv created 2010/09/15 · arxiv updated 2010/09/16

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.

Related

• The structure of a symplectic manifold on the space of loops of 7-manifold
• Loop space of a Kähler manifold
• Nonlinear Sigma Models and Symplectic Geometry on Loop Spaces of (Pseudo)Riemannian Manifolds
• Constructing Smooth Loop Spaces
• Contact Path Geometries