| 摘 要： | 正On the vortex filament in 3-spaces and its generalizations Qing Ding Shiping Zhong Abstract In this article,we devote to a mathematical survey on the theory of the vortex filament in 3-dimensional spaces and its generalizations.We 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 structures.It 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 G_2 structure on S~6.As a new result in this survey,we describe the equation of generalized bi-Schrodinger flows from R~1 into a Riemannian surface.
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