These notes give an informal and leisurely introduction to geometry for beginners. A special emphasis is placed on understanding the special linear algebraic structure in 7 dimensions that is the pointwise model for geometry, using the octonions. The basics of -structures are introduced, from a Riemannian geometric point of view, including a discussion of the torsion and its relation to curvature for a general -structure, as well as the connection to Riemannian holonomy. The history and properties of torsion-free manifolds are considered, and we stress the similarities and differences with Kähler and Calabi–Yau manifolds. The notes end with a brief survey of three important theorems about compact torsion-free manifolds.
CITATION STYLE
Karigiannis, S. (2020). Introduction to G2 Geometry. In Fields Institute Communications (Vol. 84, pp. 3–50). Springer. https://doi.org/10.1007/978-1-0716-0577-6_1
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