Spin-harmonic structures and nilmanifolds
Differential Geometry
2022-01-17 v2
Abstract
We introduce spin-harmonic structures, a class of geometric structures on Riemannian manifolds of low dimension which are defined by a harmonic unitary spinor. Such structures are related to SU(2) (dim=4,5), SU(3) (dim=6) and G_2 (dim=7) structures; in dimension 8, a spin-harmonic structure is equivalent to a balanced Spin(7) structure. As an application, we obtain examples of compact 8-manifolds endowed with non-integrable Spin(7) structures of balanced type.
Keywords
Cite
@article{arxiv.1904.01462,
title = {Spin-harmonic structures and nilmanifolds},
author = {Giovanni Bazzoni and Lucia Martin-Merchan and Vicente Munoz},
journal= {arXiv preprint arXiv:1904.01462},
year = {2022}
}
Comments
33 pages, no figures. Accepted in Communications in Analysis and Geometry