WANG Yan-bo 1 , JIANG Guang-feng 2 (1.Institute of Communications Engineering,PLA University of Science and Technology,Nanjing 210016,China; 2.Department of Mathematics and Information Science,Beijing University of Ch...WANG Yan-bo 1 , JIANG Guang-feng 2 (1.Institute of Communications Engineering,PLA University of Science and Technology,Nanjing 210016,China; 2.Department of Mathematics and Information Science,Beijing University of Chemical Technology,Beijing 100029,P.R.China)展开更多
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 ...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.展开更多
基金The research of the second author was supported by BUCTNSFC( 199871974) The second named author is the correspondent
文摘WANG Yan-bo 1 , JIANG Guang-feng 2 (1.Institute of Communications Engineering,PLA University of Science and Technology,Nanjing 210016,China; 2.Department of Mathematics and Information Science,Beijing University of Chemical Technology,Beijing 100029,P.R.China)
文摘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.
