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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.
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.
| Item Type: | Journal Article, refereed, original work |
|---|---|
| Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |
| Dewey Decimal Classification: | 510 Mathematics |
| Scopus Subject Areas: | Physical Sciences > Analysis
Social Sciences & Humanities > Political Science and International Relations Physical Sciences > Geometry and Topology |
| Language: | English |
| Date: | 2007 |
| Deposited On: | 09 Apr 2009 20:21 |
| Last Modified: | 06 Jan 2025 04:35 |
| Publisher: | Springer |
| ISSN: | 0232-704X |
| Additional Information: | The original publication is available at www.springerlink.com |
| OA Status: | Green |
| Publisher DOI: | https://doi.org/10.1007/s10455-006-9042-8 |
Constantin, A