| KdV GEOMETRIC FLOWS ON KAHLER MANIFOLDS | |
Sun, Xiaowei; Wang, Youde
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| 2011-10-01 | |
| Source Publication | INTERNATIONAL JOURNAL OF MATHEMATICS
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| ISSN | 0129-167X |
| Volume | 22Issue:10Pages:1439-1500 |
| Abstract | In this paper, we define a kind of KdV (Korteweg-de Vries) geometric flow for maps from a real line R or a circle S(1) into a Kahler manifold (N, J, h) with complex structure J and metric h as the generalization of the vortex filament dynamics from a real line or a circle. By Hasimoto transformation, we find that the KdV geometric flow on a Riemann surface of constant Gauss curvature is just classical complex-valued mKdV equation. From the view point of geometric analysis we show that the Cauchy problems of KdV flow on a Kahler manifold admits a unique local solution in suitable Sobolev spaces. In the case the target manifold (N, J, h) with complex structure J and metric h is a certain type of locally Hermitian symmetric space, we show that the KdV flow exists globally by exploiting the conservation laws and semi-conservation law of KdV flow. |
| Keyword | KdV geometric flow conversation law semi-conversation law Hasimoto transformation geometric energy method |
| DOI | 10.1142/S0129167X11007276 |
| Language | 英语 |
| Funding Project | 973 project of China[2006CB805902] ; NSFC[10990013] |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics |
| WOS ID | WOS:000296619100004 |
| Publisher | WORLD SCIENTIFIC PUBL CO PTE LTD |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/13135 |
| Collection | 数学所 |
| Corresponding Author | Sun, Xiaowei |
| Affiliation | Chinese Acad Sci, Acad Math & Syst Sci, Inst Math, Beijing 100190, Peoples R China |
| Recommended Citation GB/T 7714 | Sun, Xiaowei,Wang, Youde. KdV GEOMETRIC FLOWS ON KAHLER MANIFOLDS[J]. INTERNATIONAL JOURNAL OF MATHEMATICS,2011,22(10):1439-1500. |
| APA | Sun, Xiaowei,&Wang, Youde.(2011).KdV GEOMETRIC FLOWS ON KAHLER MANIFOLDS.INTERNATIONAL JOURNAL OF MATHEMATICS,22(10),1439-1500. |
| MLA | Sun, Xiaowei,et al."KdV GEOMETRIC FLOWS ON KAHLER MANIFOLDS".INTERNATIONAL JOURNAL OF MATHEMATICS 22.10(2011):1439-1500. |
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