Pseudoholomorphic curves in S^6 and S^5
- The octonionic cross product on R7 induces a nearly Kähler structure on S6, the analogue of the Kähler structure of S2 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 S6 and (beyond Hashimoto's work) S5. Instead of the Maurer–Cartan equations we use an embedding theorem into homogeneous spaces (here: S6=G2/SU3) involving the canonical connection.