Reducibility in Sasakian geometry

Boyer, Charles; Huang, Hongnian; Legendre, Eveline; Tønnesen-Friedman, Christina

doi:10.1090/tran/7526

Reducibility in Sasakian geometry
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by Charles P. Boyer, Hongnian Huang, Eveline Legendre and Christina W. Tønnesen-Friedman PDF

Trans. Amer. Math. Soc. 370 (2018), 6825-6869 Request permission

Abstract:

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.

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