The tensile strength of rocks plays a noteworthy role in their failure mechanism, and its determination can be beneficial in optimizing the design of the rock structures. Schistose rocks due to their inherent anisotropy in different foliation directions show a diverse strength at each direction. The purpose of this work was to compare and assess the tensile strength of phyllite, which was obtai...

We consider a partially hyperbolic diffeomorphism of a compact smooth manifold preserving a smooth measure. Assuming that the central distribution is integrable to a foliation with compact smooth leaves we show that this foliation fails to have the absolute continuity property provided that the sum of Lyapunov exponents in the central direction is not zero on a set of positive measure. We also ...

Abstract. A formula is given for the variation of the Hawking energy along any oneparameter foliation of compact spatial 2-surfaces. A surface for which one null expansion is positive and the other negative has a preferred orientation, with a spatial or null normal direction being called outgoing or ingoing as the area increases or decreases respectively. A natural way to propagate such a surfa...

Roussarie and Thurston [Ro], [Th] showed that given a taut foliation F and an incompressible torus T in a 3-manifold M , the torus may be isotoped so that it is either transverse to the leaves of the foliation, or is equal to one of the leaves of the foliation. This result was known to be false in the more general context of a foliation F without Reeb components. The only obstruction, however [...

In this paper we discuss some structure problems regarding the foliation of Levi flat manifolds, i.e. those CR manifolds which are foliated by complex leaves or, equivalently, whose Levi form vanishes. Levi flat manifolds have a particular significance among CR manifolds, since due to their degenerate nature they often behave as “limit case”, or they are an obstruction in extension problems of ...

the geometry of a system of second order differential equations is the geometry of a semispray, which is a globally defined vector field on tm. the metrizability of a given semispray is of special importance. in this paper, the metric associated with the semispray s is applied in order to study some types of foliations on the tangent bundle which are compatible with sode structure. indeed, suff...