Surveys in Differential Geometry
Volume 16 (2011)
Geometric structures on Riemannian manifolds
Pages: 161 – 264
In this article, we describe various geometries on Riemannian manifolds via a unified approach using normed division algebras and vector cross products. They include Kähler geometry, Calabi-Yau geometry, hyperkähler geometry, G2-geometry, and geometry of Riemannian symmetric spaces.