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On geodesic exponential maps of the Virasoro group


Constantin, A; Kappeler, T; Kolev, B; Topalov, P (2007). On geodesic exponential maps of the Virasoro group. Annals of Global Analysis and Geometry, 31(2):155-180.

Abstract

We study the geodesic exponential maps corresponding to Sobolev type right-invariant (weak) Riemannian metrics μ(k) (k≥ 0) on the Virasoro group Vir and show that for k≥ 2, but not for k = 0,1, each of them defines a smooth Fréchet chart of the unital element e ∈Vir. In particular, the geodesic exponential map corresponding to the Korteweg–de Vries (KdV) equation (k = 0) is not a local diffeomorphism near the origin.

Abstract

We study the geodesic exponential maps corresponding to Sobolev type right-invariant (weak) Riemannian metrics μ(k) (k≥ 0) on the Virasoro group Vir and show that for k≥ 2, but not for k = 0,1, each of them defines a smooth Fréchet chart of the unital element e ∈Vir. In particular, the geodesic exponential map corresponding to the Korteweg–de Vries (KdV) equation (k = 0) is not a local diffeomorphism near the origin.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2007
Deposited On:09 Apr 2009 20:21
Last Modified:05 Apr 2016 13:11
Publisher:Springer
ISSN:0232-704X
Additional Information:The original publication is available at www.springerlink.com
Publisher DOI:https://doi.org/10.1007/s10455-006-9042-8

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