KdV GEOMETRIC FLOWS ON KAHLER MANIFOLDS

doi:10.1142/S0129167X11007276

CORC > 数学与系统科学研究院 > 中国科学院数学与系统科学研究院 > 数学所

	KdV GEOMETRIC FLOWS ON KAHLER MANIFOLDS
	Sun, Xiaowei; Wang, Youde
刊名	INTERNATIONAL JOURNAL OF MATHEMATICS
	2011-10-01
卷号	22 期号:10 页码:1439-1500
关键词	KdV geometric flow conversation law semi-conversation law Hasimoto transformation geometric energy method
ISSN号	0129-167X
DOI	10.1142/S0129167X11007276
英文摘要	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.
资助项目	973 project of China[2006CB805902] ; NSFC[10990013]
WOS研究方向	Mathematics
语种	英语
出版者	WORLD SCIENTIFIC PUBL CO PTE LTD
WOS记录号	WOS:000296619100004
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/13134]
专题	数学所
通讯作者	Sun, Xiaowei
作者单位	Chinese Acad Sci, Acad Math & Syst Sci, Inst Math, Beijing 100190, Peoples R China
推荐引用方式 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.