Speaker
Christina Tønnesen-Friedman, Union College
Abstract
The Sasaki join construction for Sasaki manifolds was developed by C. P. Boyer, K. Galicki, and L. Ornea. It has historically been utilized to construct new examples of Sasaki metrics that are Einstein, has constant scalar curvature (CSC), or, more generally, are extremal, as defined by C. P. Boyer, K. Galicki, and S. R. Simanca.
It is reasonable to ask the following question: Suppose two Sasaki manifolds each admit at least one ray of CSC Sasaki metrics in their respective Sasaki cones. Will the Sasaki cone of a join of these two Sasaki manifolds then also admit a CSC Sasaki ray?
In this talk, which is mostly based on recent joint work with C.P. Boyer, we will see by counterexample that the general answer to this question is “no.”” However, we will also see cases where the existence of a CSC Sasaki ray survives the join construction.