2019/09/30 by Spiro Karigiannis
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Algebra over a field #Algebraic number #Connection (principal bundle) #Curvature #Geometric Analysis and Curvature Flows #Geometry #Geometry and complex manifolds #Holonomy #Mathematical analysis #Mathematics #Pointwise #Pure mathematics #Riemannian geometry #Torsion (gastropod) #math.DG
paper · pdf · doi:10.1007/978-1-0716-0577-6_1
published as Lectures and Surveys on G2-Manifolds and Related Topics (Fields Institute Communications, vol 84), p. 3-50, Springer, 2020 · 37 pages. To appear in a forthcoming volume of the Fields Institute Communications, entitled "Lectures and Surveys on G2 manifolds and related topics". Version 2: Corrected the references. No other changes
openalex publication_date 2020/01/01 · arxiv created 2020/03/28 · arxiv updated 2020/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
These notes give an informal and leisurely introduction to G2 geometry for beginners. A special emphasis is placed on understanding the special linear algebraic structure in 7 dimensions that is the pointwise model for G2 geometry, using the octonions. The basics of G2-structures are introduced, from a Riemannian geometric point of view, including a discussion of the torsion and its relation to curvature for a general G2-structure, as well as the connection to Riemannian holonomy. The history and properties of torsion-free G2 manifolds are considered, and we stress the similarities and differences with Kahler and Calabi-Yau manifolds. The notes end with a brief survey of three important theorems about compact torsion-free G2 manifolds.