On the Geometry of the Virasoro-bott Group
نویسندگان
چکیده
We consider a natural Riemannian metric on the infinite dimensional manifold of all embeddings from a manifold into a Riemannian manifold, and derive its geodesic equation in the case Emb(R, R) which turns out to be Burgers’ equation. Then we derive the geodesic equation, the curvature, and the Jacobi equation of a right invariant Riemannian metric on an infinite dimensional Lie group, which we apply to Diff(R), Diff(S), and the Virasoro-Bott group. Many of these results are well known, the emphasis is on conciseness and clarity. Table of contents
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