Surveys in Differential Geometry

Volume 16 (2011)

Geometric structures on Riemannian manifolds

Pages: 161 – 264

DOI: https://dx.doi.org/10.4310/SDG.2011.v16.n1.a5

Author

Naichung Conan Leung (The Institute of Mathematical Sciences and Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong)

Abstract

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.

Published 15 March 2013