1. Geometric structures on loop and path spaces
- Author
-
Francisco Presas and Vicente Muñoz
- Subjects
Loop (topology) ,symbols.namesake ,General Mathematics ,Loop space ,symbols ,Hermitian manifold ,Kähler manifold ,Riemannian manifold ,Fundamental theorem of Riemannian geometry ,Topology ,Pseudo-Riemannian manifold ,Mathematics ,Statistical manifold - Abstract
The loop space associated to a Riemannian manifold admits a quasisymplectic structure (that is, a closed 2-form which is non-degenerate up to a finite-dimensional kernel). We show how to construct a compatible almost-complex structure. Finally conditions to have contact structures on loop spaces are studied.
- Published
- 2010
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