Projective structure and integrable geodesic flows on the extension of Bott-Virasoro group
This is a sequel to our paper (Lett. Math. Phys. (2000)), triggered from a question posed by Marcel, Ovsienko, and Roger in their paper (1997). In this paper, we show that the multicomponent (or vector) Ito equation, modified dispersive water wave equation, and modified dispersionless long wave equa...
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Wiley
2004-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171204406553 |
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| author | Partha Guha |
| author_facet | Partha Guha |
| author_sort | Partha Guha |
| collection | DOAJ |
| description | This is a sequel to our paper (Lett. Math. Phys. (2000)), triggered from a question posed by Marcel, Ovsienko, and Roger in their paper (1997). In this paper, we show that the multicomponent (or vector) Ito equation, modified dispersive water wave equation, and modified dispersionless long wave equation are the geodesic flows with respect to an L2 metric on the semidirect product space Diffs(S1)⋉C∞(S1)kˆ, where Diffs(S1) is the group of orientation preserving Sobolev Hs diffeomorphisms of the circle. We also study the projective structure associated with the matrix Sturm-Liouville operators on the circle. |
| format | Article |
| id | doaj-art-1c62cb371f7a471fb38c1706cbaa94cb |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2004-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-1c62cb371f7a471fb38c1706cbaa94cb2025-02-03T05:44:49ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252004-01-012004713901391610.1155/S0161171204406553Projective structure and integrable geodesic flows on the extension of Bott-Virasoro groupPartha Guha0S.N. Bose National Centre for Basic Sciences, JD Block, Sector III, Calcutta 700098, IndiaThis is a sequel to our paper (Lett. Math. Phys. (2000)), triggered from a question posed by Marcel, Ovsienko, and Roger in their paper (1997). In this paper, we show that the multicomponent (or vector) Ito equation, modified dispersive water wave equation, and modified dispersionless long wave equation are the geodesic flows with respect to an L2 metric on the semidirect product space Diffs(S1)⋉C∞(S1)kˆ, where Diffs(S1) is the group of orientation preserving Sobolev Hs diffeomorphisms of the circle. We also study the projective structure associated with the matrix Sturm-Liouville operators on the circle.http://dx.doi.org/10.1155/S0161171204406553 |
| spellingShingle | Partha Guha Projective structure and integrable geodesic flows on the extension of Bott-Virasoro group International Journal of Mathematics and Mathematical Sciences |
| title | Projective structure and integrable geodesic flows on the extension of Bott-Virasoro group |
| title_full | Projective structure and integrable geodesic flows on the extension of Bott-Virasoro group |
| title_fullStr | Projective structure and integrable geodesic flows on the extension of Bott-Virasoro group |
| title_full_unstemmed | Projective structure and integrable geodesic flows on the extension of Bott-Virasoro group |
| title_short | Projective structure and integrable geodesic flows on the extension of Bott-Virasoro group |
| title_sort | projective structure and integrable geodesic flows on the extension of bott virasoro group |
| url | http://dx.doi.org/10.1155/S0161171204406553 |
| work_keys_str_mv | AT parthaguha projectivestructureandintegrablegeodesicflowsontheextensionofbottvirasorogroup |