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arXiv · 0912.0492

Kahler-Sasaki geometry of toric symplectic cones in action-angle coordinates

Miguel Abreu
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Abstract

In the same way that a contact manifold determines and is determined by a symplectic cone, a Sasaki manifold determines and is determined by a suitable Kahler cone. Kahler-Sasaki geometry is the geometry of these cones. This paper presents a symplectic action-angle coordinates approach to toric Kahler geometry and how it was recently generalized, by Burns-Guillemin-Lerman and Martelli-Sparks-Yau, to toric Kahler-Sasaki geometry. It also describes, as an application, how this approach can be used to relate a recent new family of Sasaki-Einstein metrics constructed by Gauntlett-Martelli-Sparks-Waldram in 2004, to an old family of extremal Kahler metrics constructed by Calabi in 1982.

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Miguel Abreu. 2010-02-17. Kahler-Sasaki geometry of toric symplectic cones in action-angle coordinates. https://arxiv.org/abs/0912.0492

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