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New geometric flows on Riemannian manifolds and applications to Schrodinger-Airy flows
Alternative TitleNew geometric flows on Riemannian manifolds and applications to Schrodinger-Airy flows
Sun XiaoWei1; Wang YouDe2
2014
Source PublicationSCIENCE CHINA-MATHEMATICS
ISSN1674-7283
Volume57Issue:11Pages:2247-2272
AbstractIn 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.
Other AbstractIn 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.
KeywordLANDAU-LIFSHITZ EQUATION GLOBAL WELL-POSEDNESS VORTEX FILAMENT SOLITON MAPS KDV new geometric flow Schrodinger-Airy flow global existence
Indexed ByCSCD
Language英语
Funding Project[National Natural Science Foundation of China]
CSCD IDCSCD:5267828
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/55504
Collection中国科学院数学与系统科学研究院
Affiliation1.北京大学
2.中国科学院数学与系统科学研究院
Recommended Citation
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.
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