On the vortex filament in 3-spaces and its generalizations

作     者：Qing Ding Shiping Zhong Qing Ding;Shiping Zhong

作者机构：School of Mathematical SciencesFudan UniversityShanghai 200433China School of Mathematics and Computer SciencesGannan Normal UniversityGanzhou 341000China 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2021年第64卷第7期

页      面：1331-1348页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：The first author was supported by National Natural Science Foundation of China(Grant Nos.11531012 11926307 and 12071080) 

主　　题：moving curve bi-Schrdinger flow para-complex structure almost complex structure 

摘      要：In this article,we devote to a mathematical survey on the theory of the vortex filament in 3-dimensional spaces and its *** shall present some effective geometric tools applied in the study,such as the Schrodinger flow,the geometric Korteweg-de Vries(KdV)flow and the generalized bi-Schrodinger flow,as well as the complex and para-complex *** should be mentioned that the investigation in the imaginary part of the octonions looks very fascinating,since it relates to almost complex structures and the G2 structure on S^(6).As a new result in this survey,we describe the equation of generalized bi-Schr?dinger flows from R1 into a Riemannian surface.