<ImageObject Color="BlackWhite" FileRef="13662_2018_1765_Article_IEq1.gif" Format="GIF" Rendition="HTML" Type="Linedraw"/> Spin ( 7 ) $\operatorname{Spin}(7)$ -structure equation and the vector elliptic Liouville equation
 作者： Shiping Zhong 作者单位： 1School of Mathematical Sciences, Fudan University 刊名： Advances in Difference Equations, 2018, Vol.2018 (1), pp.1-13 来源数据库： Springer Journal DOI： 10.1186/s13662-018-1765-x 关键词： Spin ( 7 ) $\operatorname{Spin}(7)$ -structure equation;  Octonions;  Almost complex structure;  The vector elliptic Liouville equation; 英文摘要： Abstract(#br)The mapping between Belavin–Polyakov (BP) equation for the evolution of a unit tangent vector T ∈ S 2 $T\in \mathbb{S}^{2}$ of a space curve in R 3 $\mathbb{R}^{3}$ and the elliptic Liouville equation has been shown by Balakrishnan (see Phys. Lett. A 204:243–246, 1995 ). In the present work, this result is effectively extended by mapping the BP equation for the unit tangent T ∈ S 6 $T\in \mathbb{S}^{6}$ of a space... curve in R 7 $\mathbb{R}^{7}$ to the vector elliptic Liouville equation. To show this correspondence, Spin ( 7 ) $\operatorname{Spin}(7)$ -frame field on the curve is used.