Reducibility in Sasakian geometry

The purpose of this paper is to study reducibility properties in Sasakian geometry. First we give the Sasaki version of the de Rham decomposition theorem; however, we need a mild technical assumption on the Sasaki automorphism group which includes the toric case. Next we introduce the concept of con...

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Bibliographic Details
Published in:Transactions of the American Mathematical Society 2018-10, Vol.370 (10), p.6825-6869
Main Authors: BOYER, CHARLES P., HUANG, HONGNIAN, LEGENDRE, EVELINE, TØNNESEN-FRIEDMAN, CHRISTINA W.
Format: Article
Language:English
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Summary:The purpose of this paper is to study reducibility properties in Sasakian geometry. First we give the Sasaki version of the de Rham decomposition theorem; however, we need a mild technical assumption on the Sasaki automorphism group which includes the toric case. Next we introduce the concept of cone reducible and consider S^3 bundles over a smooth projective algebraic variety where we give a classification result concerning contact structures admitting the action of a 2-torus of Reeb type. In particular, we can classify all such Sasakian structures up to contact isotopy on S^3 bundles over a Riemann surface of genus greater than zero. Finally, we show that in the toric case an extremal Sasaki metric on a Sasaki join always splits.
ISSN:0002-9947
1088-6850
DOI:10.1090/tran/7526