The Sasaki Join, Hamiltonian 2-forms, and Sasaki-Einstein Metrics
Abstract
By combining the join construction from Sasakian geometry with the Hamiltonian 2-form construction from K\"ahler geometry, we recover Sasaki-Einstein metrics discovered by physicists. Our geometrical approach allows us to give an algorithm for computing the topology of these Sasaki-Einstein manifolds. In particular, we explicitly compute the cohomology rings for several cases of interest and give a formula for homotopy equivalence in one particular 7-dimensional case. We also show that our construction gives at least a two dimensional cone of both Sasaki-Ricci solitons and extremal Sasaki metrics.
Keywords
Cite
@article{arxiv.1309.7067,
title = {The Sasaki Join, Hamiltonian 2-forms, and Sasaki-Einstein Metrics},
author = {Charles P. Boyer and Christina W. Tønnesen-Friedman},
journal= {arXiv preprint arXiv:1309.7067},
year = {2014}
}
Comments
38 pages, paragraph added to introduction and Proposition 4.1 added, Proposition 4.15 corrected, Remark 5.5 added, and explanation for irregular Sasaki-Einstein structures expanded. Reference added