New geometric flows on Riemannian manifolds and applications to Schrodinger-Airy flows

CSpace

	New geometric flows on Riemannian manifolds and applications to Schrodinger-Airy flows
其他题名	New geometric flows on Riemannian manifolds and applications to Schrodinger-Airy flows
	Sun XiaoWei 1; Wang YouDe 2
	2014
发表期刊	SCIENCE CHINA-MATHEMATICS
ISSN	1674-7283
卷号	57 期号:11 页码:2247-2272
摘要	In this paper, a class of new geometric flows on a complete Riemannian manifold is defined. The new flow is related to the generalized (third order) Landau-Lifshitz equation. On the other hand it could be thought of as a special case of the Schrodinger-Airy flow when the target manifold is a Kahler manifold with constant holomorphic sectional curvature. We show the local existence of the new flow on a complete Riemannian manifold with some assumptions on Ricci tensor. Moreover, if the target manifolds are Einstein or some certain type of locally symmetric spaces, the global results are obtained.
其他摘要	In this paper, a class of new geometric flows on a complete Riemannian manifold is defined. The new flow is related to the generalized (third order) Landau-Lifshitz equation. On the other hand it could be thought of as a special case of the Schrodinger-Airy flow when the target manifold is a Kahler manifold with constant holomorphic sectional curvature. We show the local existence of the new flow on a complete Riemannian manifold with some assumptions on Ricci tensor. Moreover, if the target manifolds are Einstein or some certain type of locally symmetric spaces, the global results are obtained.
关键词	LANDAU-LIFSHITZ EQUATION GLOBAL WELL-POSEDNESS VORTEX FILAMENT SOLITON MAPS KDV new geometric flow Schrodinger-Airy flow global existence
收录类别	CSCD
语种	英语
资助项目	[National Natural Science Foundation of China]
CSCD记录号	CSCD:5267828
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/55504
专题	中国科学院数学与系统科学研究院
作者单位	1.北京大学 2.中国科学院数学与系统科学研究院
推荐引用方式 GB/T 7714	Sun XiaoWei,Wang YouDe. New geometric flows on Riemannian manifolds and applications to Schrodinger-Airy flows[J]. SCIENCE CHINA-MATHEMATICS,2014,57(11):2247-2272.
APA	Sun XiaoWei,&Wang YouDe.(2014).New geometric flows on Riemannian manifolds and applications to Schrodinger-Airy flows.SCIENCE CHINA-MATHEMATICS,57(11),2247-2272.
MLA	Sun XiaoWei,et al."New geometric flows on Riemannian manifolds and applications to Schrodinger-Airy flows".SCIENCE CHINA-MATHEMATICS 57.11(2014):2247-2272.