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- Title
Path space and free loop space.
- Authors
Lim, Adrian P. C.
- Abstract
Riemannian geometry on the space of (continuous) paths in a manifold M has been studied by Cruzeiro and Malliavin. I will use concepts in path space analysis to define a Levi-Civita connection on free loop space, using the G0 metric. A tangent vector X at a loop g is a vector field along g such that X(s) ϵ Tγ(s)M. Following closely the calculations done by Fang, the Riemannian curvature RLM is given by RLM(X,Y)Z(∙) = RM(X(∙),Y(∙))Z(∙).
- Subjects
RIEMANNIAN geometry; VECTOR fields; LOOP spaces; VECTOR analysis; COMPLEX variables
- Publication
Bulletin of the Belgian Mathematical Society - Simon Stevin, 2011, Vol 18, Issue 2, p353
- ISSN
1370-1444
- Publication type
Article
- DOI
10.36045/bbms/1307452085