Harmonic $SU(3)$- and $G_2$-structures via spinors

Abstract

In this note, using the spinorial description of $SU(3)$ and $G_2$-structures obtained recently by other authors, we give necessary and sufficient conditions for harmonicity of above mentioned structures. We describe obtained results on appropriate homogeneous spaces. Here, harmonicity means harmonicity of the unique section induced by a $G$-structure in consideration.

14 pages; minor corrections

References in corpus (2)

• The Srni lectures on non-integrable geometries with torsion
• Almost Hermitian Structures with Parallel Torsion