Homogeneous Sasakian and 3-Sasakian Structures from the Spinorial Viewpoint
arXiv:2208.09301 · doi:10.1016/j.aim.2024.109493
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.
Accepted 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