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 Rn into the cosets x + Rp of the standardly embedded subspace Rp.

Foliation, as it forms generally perpendicular to the direction of principal stress, records the direction of shortening. This is related to the axis of folds, which generally form an axial-planar foliation within their axial regions.

2024年8月22日 · The rock in the upper left of Figure 10.8 is foliated, and the microscopic structure of the same type of foliated rock is shown in the photograph beneath it. Over all, the photomicrograph shows that the rock is dominated by elongated crystals aligned in bands running from the upper left to the lower right.

The diagram below shows folds forming during an early stage of regional metamorphism, along with development of foliation, in response to normal stress. The photograph below shows high-grade metamorphic rock that has undergone several stages of foliation development and folding during regional metamorphism, and may even have reached such a high ...

2024年6月8日 · A foliation of a manifold X is a decomposition into submanifolds. These submanifolds are called the leaves of the foliation and one says that X is foliated by the leaves. In order to have a useful notion, leaves are required to behave sufficiently well locally.

Many examples are illustrated on the diagram on this page. The presence of foliations/oriented fabric elements, make the resulting rock anisotropic, i.e. characterized by different physical properties depending on the direction of examination, setting foliated rocks apart from unfoliated, isotropic rocks, in which minerals are randomly oriented ...

The foliations are defined by (a) compositional layering, (b) grainsize variation, (c) parallel discontinuities, (d) preferred orientation of crystals, (e) preferred orientation of platy minerals...

We study a class of graph foliated spaces, or graph matchbox manifolds, initially constructed by Kenyon and Ghys. For graph foliated spaces we introduce a quantifier of dynamical complexity...

A discussion of foliation covers types of stress and the development of foliated rocks from slate to gneiss. Five modes of metamorphic differentiation are introduced including preservation of original compositional layering, transposition of original bedding, solution and re-precipitation, preferential nucleation, and migmatization.

Foliations were observed in the granitic gneiss, biotite gneiss and the quartzites encountered in the field (Fig. 7a, b). The gneisses have very thin and average foliation thickness of about 1-9...