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On the twistor space of the six-sphere

Published online by Cambridge University Press:  17 April 2009

Emilio Musso
Emilio Musso
Affiliation:
Dipartimento di Matematica Pure ed Applicata, Universita Dell-Aquila, via Roma 33, 67–100 L'aquila, Italy
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Abstract

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The set of all complex lines of the right-handed Dirac spinor bundle of a standard six-sphere is the total space of the twistor fibration. The twistor space, endowed with its natural Kähler 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 fiber-preserving isometries. We use a result due to Berard-Bérgery and Matsuzawa to show the existence of a non-Kähler, non symmetric, Hermitian-Einstein metric on the six-quadric, which is Spin(7)-invariant.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 39 , Issue 1 , February 1989 , pp. 119 - 127
Copyright
Copyright © Australian Mathematical Society 1989

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