Constructions in Sasakian geometry

DOI10.1007/S00209-007-0151-2zbMATH Open1134.53021arXivmath/0602233OpenAlexW2128150337MaRDI QIDQ2458873

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Publication date: 5 November 2007

Published in: (Search for Journal in Brave)

Abstract: 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 $S^{2}imes{S}^5.$ 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.

Full work available at URL: https://arxiv.org/abs/math/0602233

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