2014/04/15 by Charles P. Boyer, Boyer, Charles P., Christina W. Tønnesen-Friedman +1
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG #math.SG #msc:53D42
paper · pdf · doi:10.48550/arxiv.1404.3999
23 pages
arxiv created 2014/04/15 · arxiv updated 2014/04/16
We study a class of simply connected manifolds in all odd dimensions greater than 3 that exhibit an infinite number of toric contact structures of Reeb type that are inequivalent as contact structures. We compute the cohomology ring of our manifolds by using the join construction for Sasaki manifolds and show that all such contact structures admit a ray of compatible Sasaki metrics of constant scalar curvature (CSC). Furthermore, infinitely many such structures admit at least 3 rays of constant scalar curvature Sasaki metrics.