Some Notes on G_2 and Spin(7) Geometry

Abstract

We collect together various facts about G_2 and Spin(7) geometry which are likely well known but which do not seem to have appeared explicitly in the literature before. These notes should be useful to graduate students and new researchers in G_2 and Spin(7) geometry.

17 pages, no figures; expository notes. For version 2: Typos corrected, and added a new section on the curl and Dirac operator for G_2 structures. To appear in the Proceedings of the 2007 International Conference on Geometric Analysis. Version 3: Corrected three minor typos

References in corpus (2)

• Flows of G_2 Structures, I
• The exceptional holonomy groups and calibrated geometry

Cited by in corpus (10)

• Flows of G_2 Structures, I
• G2-structures and octonion bundles
• A new construction of compact torsion-free $G_2$-manifolds by gluing families of Eguchi-Hanson spaces
• $G_2$-structures and quantization of non-geometric M-theory backgrounds
• Deformation theory of G_2 conifolds
• Noether's Theorem in Multisymplectic Geometry
• Introduction to ${\mathrm{G}}_2$ geometry
• G2-structures for N=1 supersymmetric AdS4 solutions of M-theory
• Deformation theory of nearly ${\mathrm{G}}_2$ manifolds
• Minimal Surfaces in G2 Manifolds