Examples of singularity models for $\mathbb{Z}/2$ harmonic 1-forms and spinors in dimension 3

zbMATH Open1472.53060arXiv2001.00227MaRDI QIDQ4988703

Author name not available (Why is that?)

Publication date: 18 May 2021

Abstract: We use the symmetries of the tetrahedron, octahedron and icosahedron to construct local models for a

m a t h b b Z / 2

harmonic 1-form or spinor in 3-dimensions near a singular point in its zero loci. The local models are

m a t h b b Z / 2

harmonic 1-forms or spinors on

m a t h b b R^{3}

that are homogeneous with respect to rescaling of

m a t h b b R^{3}

with their zero locus consisting of four or more rays from the origin. The rays point from the origin to the vertices of a centered tetrahedron in one example; and they point from those of a centered octahedron and a centered icosahedron in two others.

Full work available at URL: https://arxiv.org/abs/2001.00227

zbMATH Keywords

symmetries octahedron icosahedron tetrahedron harmonic 1-form or spinor

Mathematics Subject Classification ID

Spin and Spin({}^c) geometry (53C27) Differential geometric aspects of harmonic maps (53C43)