3-Sasakian manifolds (Q2771293)

This is a review chapter on 3-Sasakian manifolds. First, there are presented definitions, notions and fundamental properties of Sasakian, Sasakian-Einstein and 3-Sasakian manifolds. Then the geometry of the foliations on these manifolds are discussed and a classification of homogeneous structures is given. There are enclosed many important results on Betti numbers of Sasakian and 3-Sasakian manifolds, Killing spinors, \(G_2\)-structures, 3-Sasakian quotient construction and toric 3-Sasakian manifolds. The last part of the paper contains open problems, questions and conjectures followed by an appendix on fundamentals of orbifolds. The reader will find a brief history of 3-Sasakian structures and 134 items as references.NEWLINENEWLINEFor the entire collection see [Zbl 0961.00021].