Curvature of the Virasoro-Bott group

Simple item page
dc.creatorMichor, Peter W.
dc.creatorRatiu, Tudor
dc.date1998-01-26
dc.date.accessioned2026-07-07T05:23:41Z
dc.date.available2026-07-07T05:23:41Z
dc.descriptionWe 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 $\Emb(\Bbb R,\Bbb R)$ 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 $\Diff(\Bbb R)$, $\Diff(S^1)$, and the Virasoro-Bott group. Many of these results are well known, the emphasis is on conciseness and clarity.
dc.descriptionAmSTeX, 16 p. To appear in J. of Lie Theory
dc.identifierhttps://arxiv.org/abs/math/9801115
dc.identifierhttp://arxiv.org/abs/math/9801115
dc.identifierJournal of Lie Theory, Vol. 8, 293-309 (1998)
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/76534
dc.subjectDifferential Geometry
dc.subject58D05, 58F07, Secondary 35Q53
dc.titleCurvature of the Virasoro-Bott group
dc.typetext

Files

Collections

arXiv