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arXiv · 1904.01462

Spin-harmonic structures and nilmanifolds

Giovanni Bazzoni·Lucia Martin-Merchan·Vicente Munoz
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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.

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Giovanni Bazzoni, Lucia Martin-Merchan, Vicente Munoz. 2019-04-02. Spin-harmonic structures and nilmanifolds. https://arxiv.org/abs/1904.01462

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