Invariant Spinors on Homogeneous Spheres
Abstract
Using the characterization of the spin representation in terms of exterior forms, we give a complete classification of invariant spinors on the nine homogeneous realizations of the sphere . In each of the cases we determine the dimension of the space of such spinors, give their explicit description, and study the underlying related geometric structures depending on the metric. We recover some known results in the Sasaki and 3-Sasaki cases and find several new examples: in particular we give the first known examples of generalized Killing spinors with four distinct eigenvalues.
Cite
@article{arxiv.2203.02961,
title = {Invariant Spinors on Homogeneous Spheres},
author = {Ilka Agricola and Jordan Hofmann and Marie-Amélie Lawn},
journal= {arXiv preprint arXiv:2203.02961},
year = {2023}
}
Comments
v3: Incorporated reviewer feedback. Final version, to appear in Differential Geometry and its Applications. v2: Added Remarks 4.1 and 5.9, minor edits for clarity, corrected typos