|Location:||MSRI: Simons Auditorium|
Sasakian manifolds are special type of metric contact manifold, which can be considered to be odd dimensional analogues of K ̈ahler manifolds. Just as in K ̈ahler geometry one can define a Sasaki-extremal metric to be a critical point of the Calabi functional. In particular, constant scalar curvature Sasakian metrics are Sasaki-extremal.
We will discuss a proof that a Sasaki-extremal metric with a fixed Reeb foliation, with its transversally holomorphic structure, is unique up to diffeo-morphisms preserving the Reeb foliation with its holomorphic structure. This involves proving that the K-energy is convex along weak geodesics in the space of metrics.
These results are contained in the preprint arXiv:1511.09167.No Notes/Supplements Uploaded No Video Files Uploaded