The geometry of loop spaces I: Hs-Riemannian metrics
نویسندگان
چکیده
منابع مشابه
Riemannian Geometry on Loop Spaces
A Riemannian metric on a manifold M induces a family of Riemannian metrics on the loop space LM depending on a Sobolev space parameter. In Part I, we compute the Levi-Civita connection for these metrics. The connection and curvature forms take values in pseudodifferential operators (ΨDOs), and we compute the top symbols of these forms. In Part II, we develop a theory of Chern-Simons classes CS ...
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We verify the following three basic results on the free loop space LM . (1) We show that the set of all points, where the fundamental form on LM is nondegenerate, is an open subset. (2) The connections of a Fréchet bundle over LM can be extended to S1-central extensions and, in particular, there exist natural connections on the string structures. (3) The notion of Christoffel symbols and the cu...
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ژورنال
عنوان ژورنال: International Journal of Mathematics
سال: 2015
ISSN: 0129-167X,1793-6519
DOI: 10.1142/s0129167x15400029