Spin-harmonic structures and nilmanifolds

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Bazzoni, Giovanni and Martín-Merchán, Lucía and Muñoz, Vicente (2022) Spin-harmonic structures and nilmanifolds. (Unpublished)

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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 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.


Item Type:Article
Uncontrolled Keywords:Spinors; Geometric structures; Dirac operator; Nilmanifolds
Subjects:Sciences > Mathematics > Topology
ID Code:72993
Deposited On:12 Jul 2022 14:55
Last Modified:02 Aug 2022 08:57

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