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arXiv · 1309.7067

The Sasaki Join, Hamiltonian 2-forms, and Sasaki-Einstein Metrics

Charles P. Boyer·Christina W. Tønnesen-Friedman
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Abstract

By combining the join construction from Sasakian geometry with the Hamiltonian 2-form construction from Kähler geometry, we recover Sasaki-Einstein metrics discovered by physicists. Our geometrical approach allows us to give an algorithm for computing the topology of these Sasaki-Einstein manifolds. In particular, we explicitly compute the cohomology rings for several cases of interest and give a formula for homotopy equivalence in one particular 7-dimensional case. We also show that our construction gives at least a two dimensional cone of both Sasaki-Ricci solitons and extremal Sasaki metrics.

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Charles P. Boyer, Christina W. Tønnesen-Friedman. 2014-06-17. The Sasaki Join, Hamiltonian 2-forms, and Sasaki-Einstein Metrics. https://arxiv.org/abs/1309.7067

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