Sasakian manifold

Summary

A Sasakian manifold is an odd-dimensional Riemannian manifold whose metric cone is a Kähler manifold. It is the odd-dimensional partner of Kähler geometry, and it carries a natural contact structure and a Reeb vector field. The round odd-dimensional spheres are the basic examples. Sasaki–Einstein manifolds are of interest in the study of Einstein metrics and in physics.