S. E. Chern

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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(More)
To Ivan Koll a r on the occasion of his 60th birthday. The usual jets were introduced by C. Ehresmann as a fundamental tool in Diierential Geometry. They permit to globalize the theory of diierential systems and to give a formulation of the \innnite groups" of E. Cartan; this leads to the theory of Lie pseudogroups; initiated by C. Ehresmann, this theory(More)
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