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Sasakian Geometry$
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Charles Boyer and Krzysztof Galicki

Print publication date: 2007

Print ISBN-13: 9780198564959

Published to Oxford Scholarship Online: January 2008

DOI: 10.1093/acprof:oso/9780198564959.001.0001

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Symmetries and Sasakian Structures

Symmetries and Sasakian Structures

(p.257) Chapter 8 Symmetries and Sasakian Structures
Sasakian Geometry

Charles P. Boyer

Krzysztof Galicki

Oxford University Press

This chapter presents known results concerning symmetries of Sasakian structures, including a detailed study of the Sasakian automorphisms and various deformations of Sasakian structures. Homogeneous Sasakian geometry is developed in parallel to the better known results concerning homogeneous contact manifolds. Finally, using the notion of contact moment maps, the Sasakian and contact analogues of the well known technique of symplectic reduction is developed. The chapter ends with in important application: a study of toric contact and toric Sasakian manifolds culminating in several Delzant-type results implying that the toric structure is determined by a polyedral cone and polytope, respectively.

Keywords:   contact reduction, homogeneous Sasakian manifolds, Sasakian automorphisms, deformations of Sasakian structures, polyhedral cones, polytopes, moment map, Sasakian reduction, toric Sasakian manifolds, Delzant classification

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