Resumen de Pseudoholomorphic curves in S⁶ and S⁵

Jost Hinrich Eschenburg, Theodoros Vlachos

• The octonionic cross product on R7 induces a nearly K¨ahler structure on S 6 , the analogue of the K¨ahler structure of S 2 given by the usual (quaternionic) cross product on R3 . Pseudoholomorphic curves with respect to this structure are the analogue of meromorphic functions. They are (super-)conformal minimal immersions. We reprove a theorem of Hashimoto [Tokyo J. Math. 23 (2000), 137–159] giving an intrinsic characterization of pseudoholomorphic curves in S 6 and (beyond Hashimoto’s work) S 5 . Instead of the Maurer–Cartan equations we use an embedding theorem into homogeneous spaces (here: S 6 = G2/SU3) involving the canonical connection.