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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Reducibility in Sasakian geometry


Authors: Charles P. Boyer, Hongnian Huang, Eveline Legendre and Christina W. Tønnesen-Friedman
Journal: Trans. Amer. Math. Soc. 370 (2018), 6825-6869
MSC (2010): Primary 53C25; Secondary 53C21
DOI: https://doi.org/10.1090/tran/7526
Published electronically: June 26, 2018
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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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Additional Information

Charles P. Boyer
Affiliation: Department of Mathematics and Statistics, University of New Mexico, Albuquerque, New Mexico 87131
Email: cboyer@math.unm.edu

Hongnian Huang
Affiliation: Department of Mathematics and Statistics, University of New Mexico, Albuquerque, New Mexico 87131
Email: hnhuang@gmail.com

Eveline Legendre
Affiliation: Institut de Mathématiques de Toulouse, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse, France
Email: eveline.legendre@math.univ-toulouse.fr

Christina W. Tønnesen-Friedman
Affiliation: Department of Mathematics, Union College, Schenectady, New York 12308
Email: tonnesec@union.edu

DOI: https://doi.org/10.1090/tran/7526
Keywords: Sasakian, reducible, decomposable, join
Received by editor(s): August 11, 2016
Published electronically: June 26, 2018
Additional Notes: The first author was partially supported by a grant (#245002) from the Simons Foundation.
The third author was partially supported by France ANR project EMARKS No ANR-14-CE25-0010.
The fourth author was partially supported by grant #208799 from the Simons Foundation.
Article copyright: © Copyright 2018 American Mathematical Society

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