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.
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