We give elementary and explicit arguments to show that the geodesic ow on the unit tangent bundle of a two dimensional Riemannian manifold with constant negative curvature provides an example of a \fast" dynamo for the magnetic kinematic dynamo equation.

412 NOTICES OF THE AMS VOLUME 51, NUMBER 4 Billiards are dynamical systems. In the simplest case, a “billiard table” is a compact domain Q ⊂ Rd with a piecewise smooth boundary. For a large part of the theory the class of smoothness plays no role. The reader is invited to think about components of the boundary ∂Q as subsets of C∞-submanifolds of codimension 1. The phase space M of the billiard ...

We study the geometric properties of the base manifold for the unit tangent bundle satisfying the η-Einstein condition with the standard contact metric structure. One of the main theorems is that the unit tangent bundle of 4-dimensional Einstein manifold, equipped with the canonical contact metric structure, is ηEinstein manifold if and only if base manifold is the space of constant sectional c...

For these distributions only the leading vehicle in a platoon has its speed measured. The rationale for measuring these is to get an estimate of the desired speed of traffic at the point of measurement. The distributions in Figure 1 are of this type. They are produced by combining the results of a number of surveys at different sites into a representative distribution weighted by the traffic fl...

In this article we give a geometric interpretation of the Hitchin component T (Σ) ⊂ Rep(π1(Σ),PSL4(R)) of a closed oriented surface of genus g ≥ 2. We show that representations in T (Σ) are precisely the holonomy representations of properly convex foliated projective structures on the unit tangent bundle of Σ. From this we also deduce a geometric description of the Hitchin component T (Σ, Sp4(R...

A decoration of a hyperbolic surface finite type is choice circle, horocycle or hypercycle about each cone-point, cusp flare the surface, respectively. In this article we show that induces unique canonical tessellation and dual decomposition underlying surface. They are analogues weighted Delaunay Voronoi in Euclidean plane. We develop characterisation terms geometric equivalents Delaunay's emp...

The standard eigenfunctions φλ = ei〈λ,x〉 on flat tori Rn/L have L-norms bounded independently of the eigenvalue. In the case of irrational flat tori, it follows that L2normalized eigenfunctions have uniformly bounded L-norms. Similar bases exist on other flat manifolds. Does this property characterize flat manifolds? We give an affirmative answer for compact Riemannian manifolds with quantum co...