Instantons on the six-sphere and twistors
Abstract
We consider the six-sphere S6=G2/SU(3) and its twistor space Z=G2/U(2) associated with the SU(3)-structure on S6. It is shown that a Hermitian Yang-Mills connection (instanton) on a smooth vector bundle over S6 is equivalent to a flat partial connection on a vector bundle over the twistor space Z. The relation with Tian's tangent instantons on R7 and their twistor description are briefly discussed.
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