Sasaki geometry and positive curvature

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• Song Sun (Imperial College)
• Friday 13 April 2012, 10:30-11:30
• MR2.

If you have a question about this talk, please contact Dr. J Ross.

We classify simply connected compact Sasaki manifolds with positive transverse bisectional curvature. In particular, the moduli space of all such manifolds can be contracted to a point—the standard round sphere. This provides an alternative proof of the Mori-Siu-Yau theorem on Frankel conjecture as well as extends it to the orbifold case.

The proof involves deforming any such manifold towards the round sphere, through an infinite dimensional evolution equation followed by a finite dimensional ``volume decreasing flow”. The latter can only be done within the framework of Sasaki geometry and is inspired by the work of Martelli-Sparks-Yau on volume minimization. Time permitting we will also talk about the case when the positivity assumption is replaced by non-negativity. This talk is based on joint work with Weiyong He.

This talk is part of the Workshop on Kahler Geometry series.

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