Associative Cones and Integrable Systems  

作　　者：Chuu-Lian TERNG 

机构地区：[1]Dedicated to the memory of Shiing-Shen Chern

出　　处：《Chinese Annals of Mathematics,Series B》2006年第2期153-168,共16页数学年刊（B辑英文版）

基　　金：Partially supported by NSF grant DMS-0529756.

摘　　要：Abstract We identify R^7 as the pure imaginary part of octonions. Then the multiplication in octonions gives a natural almost complex structure for the unit sphere S^6. It is known that a cone over a surface M in S^6 is an associative submanifold of R^7 if and only if M is almost complex in S^6. In this paper, we show that the Gauss-Codazzi equation for almost complex curves in S^6 are the equation for primitive maps associated to the 6-symmetric space G2/T^2, and use this to explain some of the known results. Moreover, the equation for S^1-symmetric almost complex curves in S^6 is the periodic Toda lattice, and a discussion of periodic solutions is given.

关 键 词：OCTONIONS Associative cone Almost complex curve Primitive map 

分 类 号：O186.5[理学—数学]