The Local Moduli of Sasakian 3-Manifolds

The Newman-Penrose-Perjes formalism is applied to Sasakian 3-manifolds and the local form of the metric and contact structure is presented. The local moduli space can be parameterised by a single function of two variables and it is shown that, given any smooth function of two variables, there exists locally a Sasakian structure with scalar curvature equal to this function. The case where the scalar curvature is constant ($\eta$-Einstein Sasakian metrics) is completely solved locally. The resulting Sasakian manifolds include $S^3$, $Nil$ and $\tilde{SL_2R}$, as well as the Berger spheres. It is also shown that a conformally flat Sasakian 3-manifold is Einstein of positive scalar curvature.Comment: 9 pages, RevTeX, no figure

Birth of a station: the impact of Nova on the Perth radio market

At the end of 2002 a new player entered the Perth radio market. The launch of Nova threatened to create ripples in the relatively calm waters of the radio pool which had become comfortably settled since the last new entrant twenty years before. Researchers had a chance to observe the impact on the market, the products, the formats and the audiences and this paper describes the highs and lows of the market players during Nova's first year

Reflection of a wave off a surface

Recent advances in twistor theory are applied to geometric optics in ${\Bbb{R}}^3$. The general formulae for reflection of a wavefront in a surface are derived and in three special cases explicit descriptions are provided: when the reflecting surface is a plane, when the incoming wave is a plane and when the incoming wave is spherical. In each case particular examples are computed exactly and the results plotted to illustrate the outgoing wavefront.Comment: 14 pages, AMS-LATE

Geodesic Flow on the Normal Congruence of a Minimal Surface

We study the geodesic flow on the normal line congruence of a minimal surface in ${\Bbb{R}}^3$ induced by the neutral K\"ahler metric on the space of oriented lines. The metric is lorentz with isolated degenerate points and the flow is shown to be completely integrable. In addition, we give a new holomorphic description of minimal surfaces in ${\Bbb{R}}^3$ and relate it to the classical Weierstrass representation.Comment: AMS-LATEX 8 pages 2, figure

Minimal Lagrangian surfaces in the tangent bundle of a Riemannian surface

Given an oriented Riemannian surface $(\Sigma, g)$, its tangent bundle $T\Sigma$ enjoys a natural pseudo-K\"{a}hler structure, that is the combination of a complex structure \J, a pseudo-metric \G with neutral signature and a symplectic structure \Om. We give a local classification of those surfaces of $T\Sigma$ which are both Lagrangian with respect to \Om and minimal with respect to \G. We first show that if $g$ is non-flat, the only such surfaces are affine normal bundles over geodesics. In the flat case there is, in contrast, a large set of Lagrangian minimal surfaces, which is described explicitly. As an application, we show that motions of surfaces in $\R^3$ or $\R^3_1$ induce Hamiltonian motions of their normal congruences, which are Lagrangian surfaces in $T\S^2$ or T \H^2 respectively. We relate the area of the congruence to a second-order functional $\mathcal{F}=\int \sqrt{H^2-K} dA$ on the original surface.Comment: 22 pages, typos corrected, results streamline