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Extremal Sasakian geometry on ${T}^{2} \times {S}^{3} $ and related manifolds

Part of: Global differential geometry Symplectic geometry, contact geometry

Published online by Cambridge University Press:  03 June 2013

Charles P. Boyer  and
Christina W. Tønnesen-Friedman
Charles P. Boyer
Affiliation:
Department of Mathematics and Statistics, University of New Mexico, Albuquerque, NM 87131, USA email cboyer@math.unm.edu
Christina W. Tønnesen-Friedman
Affiliation:
Department of Mathematics, Union College, Schenectady, New York 12308, USA email tonnesec@union.edu
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Abstract

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We prove the existence of extremal Sasakian structures occurring on a countably infinite number of distinct contact structures on ${T}^{2} \times {S}^{3} $ and certain related 5-manifolds. These structures occur in bouquets and exhaust the Sasaki cones in all except one case in which there are no extremal metrics.

Keywords

extremal Sasaki metricsextremal Kähler metricsSasaki cone and Sasaki bouquetjoin construction

MSC classification

Secondary: 53D42: Symplectic field theory; contact homology 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.)
Type
Research Article
Information
Compositio Mathematica , Volume 149 , Issue 8 , August 2013 , pp. 1431 - 1456
Copyright
© The Author(s) 2013 

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