In mathematics, a foliation is a geometric device used to study manifolds, consisting of an integrable subbundle of the tangent bundle. A foliation looks locally like a decomposition of the manifold as a union of parallel submanifolds of smaller dimension.

Read more about FoliationDefinition, Foliations and Integrability, Existence of Foliations

Other articles related to "foliation":

Shear (geology) - Microstructures of Shear Zones
... During the initiation of shearing, a penetrative planar foliation is first formed within the rock mass ... The incipient shear foliation typically forms normal to the direction of principal shortening, and is diagnostic of the direction of shortening ... In symmetric shortening, objects flatten on this shear foliation much the same way that a round ball of treacle flattens with gravity ...
Existence of Foliations
... Haefliger (1970) gave a necessary and sufficient condition for a distribution on a connected non-compact manifold to be homotopic to an integrable distribution ... Thurston (1974, 1976) showed that any compact manifold with a distribution has a foliation of the same dimension ...
Cleavage (geology)
... Cleavage is a type of rock foliation, a fabric element that describes the way planar features develop in a rock ... Foliation is separated into two groups primary and secondary ... Cleavage is a type of secondary foliation associated with fine grained rocks ...