Constructions in Sasakian Geometry

Details Constructions in Sasakian Geometry Constructions in Sasakian Geometry

2006-02-10

arxiv.org/abs/math/0602233v2

Mathematische Zeitschrift 257 (2007), 907-924.

Mathematics

Differential Geometry

Some minor errors corrected. References updated. To appear in Mathematische Zeitschrift

Scientific paper

We describe various constructions in Sasakian geometry. First we generalize the join construction of the first two authors to arbitrary Sasakian manifolds. We then give several examples, including ones which prove the existence of Sasakian-Einstein metrics on manifolds homeomorphic to $S^2\times S^5.$ Then we use a generalization of the join construction due to Lerman, namely contact fibre bundles, to give a theorem constructing toric Sasakian structures. Finally, we explicitly construct regular toric Sasakian structures on all simply connected regular contact manifolds in dimension five.

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