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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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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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Additional Information
  • Charles P. Boyer
  • Affiliation: Department of Mathematics and Statistics, University of New Mexico, Albuquerque, New Mexico 87131
  • MR Author ID: 40590
  • Email: cboyer@math.unm.edu
  • Hongnian Huang
  • Affiliation: Department of Mathematics and Statistics, University of New Mexico, Albuquerque, New Mexico 87131
  • MR Author ID: 936774
  • Email: hnhuang@gmail.com
  • Eveline Legendre
  • Affiliation: Institut de Mathématiques de Toulouse, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse, France
  • MR Author ID: 903289
  • 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
  • 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.
  • © Copyright 2018 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 370 (2018), 6825-6869
  • MSC (2010): Primary 53C25; Secondary 53C21
  • DOI: https://doi.org/10.1090/tran/7526
  • MathSciNet review: 3841834