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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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Foliations

Foliations

Chapter:
(p.51) Chapter 2 Foliations
Source:
Sasakian Geometry
Author(s):

Charles P. Boyer

Krzysztof Galicki

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198564959.003.0003

As Sasakian manifolds are all examples of Riemannian foliations with one-dimensional leaves, this chapter goes into the world of foliations with a particular focus on the Riemannian case. Haeiger structures, leaf holonomy, the holonomy groupoid, and basic cohomology are introduced, focusing on the transverse geometry of Riemannian foliations, in particular, Riemannian ows. Certain invariants such as the toral rank are introduced.

Keywords:   Riemannian foliations, Haeiger structures, basic cohomology, leaf holonomy, holonomy groupoid, transverse geometry, Riemannian ows, toral rank

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