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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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K-Contact and Sasakian Structures

K-Contact and Sasakian Structures

Chapter:
(p.207) Chapter 7 K-Contact and Sasakian Structures
Source:
Sasakian Geometry
Author(s):

Charles P. Boyer

Krzysztof Galicki

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198564959.003.0008

This chapter begins the study of Sasakian geometry, where all important structure theorems are presented. It then gathers all the results concerning the geometry, topology, and curvature properties of both K-contact and Sasakian manifolds. The relation between Sasakian and algebraic geometry is stressed, as well as important invariants such as the basic cohomology groups, and the basic first Chern class that are associated to certain spaces of Sasakian structures. A main tool used in the text is the transverse Yau Theorem due to El Kacimi-Alaoui.

Keywords:   algebraic geometry, basic cohomology, basic first Chern class, K-contact manifolds, Sasakian manifolds, Sasakian structures, spaces of Sasakian structures, transverse Yau Theorem

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