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About generalized complex structures on $\mathbb S^6$
Published 9 May 2024 in math.DG | (2405.05681v3)
Abstract: We study the existence of generalized complex structures on the six-dimensional sphere $\mathbb S6$. We work with the generalized tangent bundle $\mathbb T\mathbb S6\to \mathbb S6$ 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 $\mathbb S6$ from its usual nearly K\"ahler structure inherited from the octonions product.
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