For a compact riemannian manifold of negative curvature, the geodesic foliation of its unit tangent bundle is independent of the negatively curved metric, up to Hölder bicontinuous homeomorphism. However, the riemannian metric defines a natural transverse measure to this foliation, the Liouville transverse measure, which does depend on the metric. For a surface S, we show that the map which to ...

a r t i c l e i n f o Inclusion trails in 58 garnet porphyroblasts in a single sample from the Cram Hill Formation in southeast Vermont were imaged using high-resolution X-ray computed tomography. Texturally the porphyroblasts have a large core with a sub-vertical foliation that has a well defined geometry with a mean orientation of 113/72E for a 95% confidence cone semi-angle of 5.3°. This ste...

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...

here, a finsler manifold $(m,f)$ is considered with corresponding curvature tensor, regarded as $2$-forms on the bundle of non-zero tangent vectors. certain subspaces of the tangent spaces of $m$ determined by the curvature are introduced and called $k$-nullity foliations of the curvature operator. it is shown that if the dimension of foliation is constant, then the distribution is involutive a...

Benedetti and Guadagnini [5] have conjectured that the constant mean curvature foliation Mτ in a 2 + 1 dimensional flat spacetime V with compact hyperbolic Cauchy surfaces satisfies limτ→−∞ lMτ = sT , where lMτ and sT denote the marked length spectrum ofMτ and the marked measure spectrum of the R-tree T , dual to the measured foliation corresponding to the translational part of the holonomy of ...

In relativistic space-time, Bohmian theories can be formulated by introducing a privileged foliation of space-time. The introduction of such a foliation-as extra absolute space-time structure-would seem to imply a clear violation of Lorentz invariance, and thus a conflict with fundamental relativity. Here, we consider the possibility that, instead of positing it as extra structure, the required...

Foliate systems are those which preserve some (possibly singular) foliation of phase space, such as systems with integrals, systems with continuous symmetries, and skew product systems. We study numerical integrators which also preserve the foliation. The case in which the foliation is given by the orbits of an action of a Lie group has a particularly nice structure, which we study in detail, g...