On the geometry of free loop spaces

P. Manoharan

International Journal of Mathematics and Mathematical Sciences, 2002, vol. 30, 1-9

Abstract:

We verify the following three basic results on the free loop space L M . (1) We show that the set of all points, where the fundamental form on L M is nondegenerate, is an open subset. (2) The connections of a Fréchet bundle over L M can be extended to S 1 -central extensions and, in particular, there exist natural connections on the string structures. (3) The notion of Christoffel symbols and the curvature are introduced on L M and they are described in terms of Christoffel symbols of M .

Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:561937

DOI: 10.1155/S0161171202011560

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