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2-dimensional section of Reeb foliation 3-dimensional model of Reeb foliation. In mathematics (differential geometry), a foliation is an equivalence relation on an n-manifold, the equivalence classes being connected, injectively immersed submanifolds, all of the same dimension p, modeled on the decomposition of the real coordinate space R n into the cosets x + R p of the standardly embedded ...
Foliation may be formed by realignment of micas and clays via physical rotation of the minerals within the rock. Often this foliation is associated with diagenetic metamorphism and low-grade burial metamorphism. Foliation may parallel original sedimentary bedding, but more often is oriented at some angle to it.
In geology, 3D fold evolution is the study of the full three dimensional structure of a fold as it changes in time. A fold is a common three-dimensional geological structure that is associated with strain deformation under stress. Fold evolution in three dimensions can be broadly
The foliations are symmetrically arranged with respect to the axial plane, depending on the composition and competency of a rock. For example, when mixed sandstone and mudstone sequences are folded during very-low to low grade metamorphism, cleavage forms parallel to the fold axial plane, particularly in the clay-rich parts of the sequence. In ...
For example, if a porous sandstone unit covered with low permeability shale is folded into an anticline, it may form a hydrocarbons trap, oil accumulating in the crest of the fold. Most anticlinal traps are produced as a result of sideways pressure, folding the layers of rock, but can also occur from sediments being compacted.
In mathematics, the Reeb foliation is a particular foliation of the 3-sphere, introduced by the French mathematician Georges Reeb (1920–1993). It is based on dividing the sphere into two solid tori , along a 2- torus : see Clifford torus .