The Sasaki Join, Hamiltonian 2-forms, and Constant Scalar Curvature
Abstract
We describe a general procedure for constructing new Sasaki metrics of constant scalar curvature from old ones. Explicitly, we begin with a regular Sasaki metric of constant scalar curvature on a 2n+1-dimensional compact manifold M and construct a sequence, depending on four integer parameters, of rays of constant scalar curvature (CSC) Sasaki metrics on a compact Sasaki manifold of dimension . We also give examples which show that the CSC rays are often not unique on a fixed strictly pseudoconvex CR manifold or a fixed contact manifold. Moreover, it is shown that when the first Chern class of the contact bundle vanishes, there is a two dimensional subcone of Sasaki Ricci solitons in the Sasaki cone, and a unique Sasaki-Einstein metric in each of the two dimensional sub cones.
Keywords
Cite
@article{arxiv.1402.2546,
title = {The Sasaki Join, Hamiltonian 2-forms, and Constant Scalar Curvature},
author = {Charles P. Boyer and Christina W. Tønnesen-Friedman},
journal= {arXiv preprint arXiv:1402.2546},
year = {2016}
}
Comments
32 pages. A gap in the argument of applying the admissibility conditions to irregular Sasakian structures is filled. Some minor corrections and additions are also made. This is the final version which will appear in the Journal of Geometric Analysis. It also encorporates much from our paper arXiv:1309.7067