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Constructions in Sasakian geometry. (English) Zbl 1134.53021

The authors use previously formed join constructions for quazi-regular Sasakian Einstein manifolds and generalize them to a construction for arbitrary quazi-regular Sasaskian spaces. The new construction is more flexible and naturally yields multiple examples. The authors also show how the join construction can be represented as a special case of Lerman’s contact fiber bundle construction. Previously proven results are well classified and used to further study the toric Sasakian five-dimensional manifolds. It is shown that any simply connected compact oriented five-manifold with vanishing torsion admits regular toric Sasakian structures.

MSC:

53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
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