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Instantons on the six-sphere and twistors. (English) Zbl 1278.81129
Summary: We consider the six-sphere $$S^6 = G_2/{\text SU}(3)$$ and its twistor space $${\mathcal Z}= G_2/{\text U}(2)$$ associated with the SU(3)-structure on $$S^6$$. It is shown that a Hermitian Yang-Mills connection (instanton) on a smooth vector bundle over $$S^6$$ is equivalent to a flat partial connection on a vector bundle over the twistor space $${\mathcal Z}$$. The relation with Tian’s tangent instantons on $${\mathbb{R}}^7$$ and their twistor description are briefly discussed.