Homogeneous Sasakian and 3-Sasakian Structures from the Spinorial Viewpoint

Abstract

We give a spinorial construction of Sasakian and 3-Sasakian structures in arbitrary dimension, generalizing previously known results in dimensions 5 and 7. Furthermore, we obtain a complete description of the space of invariant spinors on a homogeneous 3-Sasakian space, and show that it is spanned by the Clifford products of invariant differential forms with a certain invariant Killing spinor. Finally, we give a basis for the space of invariant Riemannian Killing spinors on a homogeneous 3-Sasakian space, and determine which of these induce the homogeneous 3-Sasakian structure.

arXiv commentAccepted for publication in Advances in Mathematics. V2: Incorporated feedback from the anonymous reviewer, updates and corrections to some results and proofs, improvements in clarity and exposition

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Cited by in corpus (1)

• The heterotic G${}_2$ system with reducible characteristic holonomy