We introduce spin-harmonic structures, a class of geometric structures on Riemannian manifolds of low dimension which are defined by a harmonic unit-length spinor. Such structures are related to SU(2) (dim = 4, 5), SU(3) (dim = 6) and G2 (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.
Spin-harmonic structures and nilmanifolds
Bazzoni G.;
2024-01-01
Abstract
We introduce spin-harmonic structures, a class of geometric structures on Riemannian manifolds of low dimension which are defined by a harmonic unit-length spinor. Such structures are related to SU(2) (dim = 4, 5), SU(3) (dim = 6) and G2 (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.
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