Some examples of toric Sasaki-Einstein manifolds
Differential Geometry
2010-07-05 v3
Abstract
A series of examples of toric Sasaki-Einstein 5-manifolds is constructed. These are submanifolds of toric 3-Sasaki 7-manifolds and such a Sasaki-Einstein 5-manifold corresponds uniquely to a toric 3-Sasaki 7-manifold. This produces examples of quasi-regular Sasaki-Einstein structures on every #k(S^2 xS^3), for k odd. Toric geometry is used to construct examples of positive Ricci curvature toric Sasaki structures on non-spin 5-manifolds. Then the join construction is used to construct infinitely many quasi-regular toric Sasaki-Einstein manifolds with arbitrarily high second Betti number in every odd dimesion >3.
Cite
@article{arxiv.math/0703501,
title = {Some examples of toric Sasaki-Einstein manifolds},
author = {Craig van Coevering},
journal= {arXiv preprint arXiv:math/0703501},
year = {2010}
}
Comments
Some minor editing made. Invited contribution to "Riemannian Topology and Geometric Structures on Manifolds", Birkh\"auser 2008