About generalized complex structures on S6

Abstract

We study the existence of generalized complex structures on the six-dimensional sphere S6. We work with the generalized tangent bundle TS6 --> S6 and define the integrability of generalized geometric structures in terms of the Dorfman bracket. Specifically, we prove that there is not a direct way to induce a generalized complex structure on S6 from its usual nearly Kähler structure inherited from the octonions product.