科研之友
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摘要
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 G(2)/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.
- 出版日期2006-3
