Sous-variétés associatives et courbes holomorphes dans S 6. (Associative submanifolds and holomorphic curves in S 6). (French) Zbl 0635.53041

Théorie des variétés minimales et applications, Sémin. Palaisau/France 1983/1984, Astérisque 154-155, 209-220 (1988).
Summary: [For the entire collection see Zbl 0635.53001.]
Here the geometry of certain minimizing submanifolds of \({\mathbb{R}}^ 7 \)and \({\mathbb{R}}^ 8 \)connected with Cayley’s octonions is studied. These submanifolds give rise to minimal immersions of compact Riemann surfaces as pseudo-holomorphic curves of S 6 as shown by R. Bryant.


53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
53C55 Global differential geometry of Hermitian and Kählerian manifolds


Zbl 0635.53001