Introduction to $\mathrm{G}_2$ geometry

@article{Karigiannis2020IntroductionT,
  title={Introduction to \$\mathrm\{G\}\_2\$ geometry},
  author={Spiro Karigiannis},
  journal={arXiv: Differential Geometry},
  year={2020},
  pages={3-50}
}
These notes give an informal and leisurely introduction to \(\mathrm {G}_2\) geometry for beginners. A special emphasis is placed on understanding the special linear algebraic structure in 7 dimensions that is the pointwise model for \(\mathrm {G}_2\) geometry, using the octonions. The basics of \(\mathrm {G}_2\)-structures are introduced, from a Riemannian geometric point of view, including a discussion of the torsion and its relation to curvature for a general \(\mathrm {G}_2\)-structure, as… Expand

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