A Riemannian foliation is a geometric structure on a Riemannian manifold where the manifold can be decomposed into a collection of disjoint submanifolds called leaves, such that the Riemannian metric is compatible with this decomposition. This means that at every point, one can find orthogonal projections from the ambient manifold to these leaves, preserving the distances within the leaves. The concept is crucial for understanding how curvature and geometry behave within the framework of foliated spaces.
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