On the twistor space of the six-sphere

Emilio Musso
1989 Bulletin of the Australian Mathematical Society  
The set of all complex lines of the right-handed Dirac spinor bundle of a standard sixsphere is the total space of the twistor fibration. The twistor space, endowed with its natural Kahler structure, is recognised to be a six-dimensional complex quadric. The relevant group is Spin (7), which acts transitively on the six-quadric, as a group of fiberpreserving isometries. We use a result due to Berard-Bergery and Matsuzawa to show the existence of a non-Kahler, non symmetric, Hermitian-Einstein
more » ... ermitian-Einstein metric on the six-quadric, which is Spin (7)-invariant.
doi:10.1017/s0004972700028021 fatcat:uswuvczqhbfwroegcuetcc7xle