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Geometric Analysis: A proof of uniqueness of Sasaki-extremal metrics April 21, 2016 (11:00 AM PDT - 12:00 PM PDT)
Parent Program: --
Location: MSRI: Simons Auditorium
Speaker(s) Craig van Coevering (University of Science and Technology of China)
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Sasakian manifolds are special type of metric contact manifold, which can be considered to be odd dimensional analogues of K ╠łahler manifolds. Just as in K ╠łahler 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.

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