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

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

Weyl-type Fields with Geodesic Lines of Force

The static electrogravitational equations are studied and it is shown that an aligned type D metric which has a Weyl-type relationship between the gravitational and electric potential has shearfree geodesic lines of force. All such fields are then found and turn out to be the fields of a charged sphere, charged infinite rod and charged infinite plate. A further solution is also found with shearing geodesic lines of force. This new solution can have $m>|e|$ or $m<|e|$, but cannot be in the Majumdar-Papapetrou class (in which $m = |e|$). It is algebraically general and has flat equipotential surfaces.Comment: 13 pages, RevTe

(In)finite extent of stationary perfect fluids in Newtonian theory

For stationary, barotropic fluids in Newtonian gravity we give simple criteria on the equation of state and the "law of motion" which guarantee finite or infinite extent of the fluid region (providing a priori estimates for the corresponding stationary Newton-Euler system). Under more restrictive conditions, we can also exclude the presence of "hollow" configurations. Our main result, which does not assume axial symmetry, uses the virial theorem as the key ingredient and generalises a known result in the static case. In the axially symmetric case stronger results are obtained and examples are discussed.Comment: Corrections according to the version accepted by Ann. Henri Poincar

Interior Weyl-type Solutions of the Einstein-Maxwell Field Equations

Static solutions of the electro-gravitational field equations exhibiting a functional relationship between the electric and gravitational potentials are studied. General results for these metrics are presented which extend previous work of Majumdar. In particular, it is shown that for any solution of the field equations exhibiting such a Weyl-type relationship, there exists a relationship between the matter density, the electric field density and the charge density. It is also found that the Majumdar condition can hold for a bounded perfect fluid only if the matter pressure vanishes (that is, charged dust). By restricting to spherically symmetric distributions of charged matter, a number of exact solutions are presented in closed form which generalise the Schwarzschild interior solution. Some of these solutions exhibit functional relations between the electric and gravitational potentials different to the quadratic one of Weyl. All the non-dust solutions are well-behaved and, by matching them to the Reissner-Nordstr\"{o}m solution, all of the constants of integration are identified in terms of the total mass, total charge and radius of the source. This is done in detail for a number of specific examples. These are also shown to satisfy the weak and strong energy conditions and many other regularity and energy conditions that may be required of any physically reasonable matter distribution.Comment: 21 pages, RevTex, to appear in General Relativity and Gravitatio

Yang's gravitational theory

Yang's pure space equations (C.N. Yang, Phys. Rev. Lett. v.33, p.445 (1974)) generalize Einstein's gravitational equations, while coming from gauge theory. We study these equations from a number of vantage points: summarizing the work done previously, comparing them with the Einstein equations and investigating their properties. In particular, the initial value problem is discussed and a number of results are presented for these equations with common energy-momentum tensors.Comment: 28 pages, to appear in Gen. Rel. Gra

The role of research experiences in developing pre-service teachers’ epistemic beliefs

Persistent concerns about the theory-practice gap and desires for an ‘evidence-informed’ teaching profession have prompted research into how teachers' epistemic beliefs influence their acceptance or rejection of educational research. This study analyses longitudinal interview data from six pre-service teachers (PSTs) to explore how experiences of conducting research (in the domains of science or education) during initial teacher education (ITE) contribute to epistemological development. These research experiences provided opportunities for ad-hoc epistemological development, even in the absence of intentional efforts. Epistemic beliefs sometimes appeared to be supplanted, counterproductively, from science to education. The implications for teacher education and research are discussed

Jasmonate promotes auxin-induced adventitious rooting in dark-grown Arabidopsis thaliana seedlings and stem thin cell layers by a cross-talk with ethylene signalling and a modulation of xylogenesis

Background: Adventitious roots (ARs) are often necessary for plant survival, and essential for successful micropropagation. In Arabidopsis thaliana dark-grown seedlings AR-formation occurs from the hypocotyl and is enhanced by application of indole-3-butyric acid (IBA) combined with kinetin (Kin). The same IBA + Kin-treatment induces AR-formation in thin cell layers (TCLs). Auxin is the main inducer of AR-formation and xylogenesis in numerous species and experimental systems. Xylogenesis is competitive to AR-formation in Arabidopsis hypocotyls and TCLs. Jasmonates (JAs) negatively affect AR-formation in de-etiolated Arabidopsis seedlings, but positively affect both AR-formation and xylogenesis in tobacco dark-grown IBA + Kin TCLs. In Arabidopsis the interplay between JAs and auxin in AR-formation vs xylogenesis needs investigation. In de-etiolated Arabidopsis seedlings, the Auxin Response Factors ARF6 and ARF8 positively regulate AR-formation and ARF17 negatively affects the process, but their role in xylogenesis is unknown. The cross-talk between auxin and ethylene (ET) is also important for AR-formation and xylogenesis, occurring through EIN3/EIL1 signalling pathway. EIN3/EIL1 is the direct link for JA and ET-signalling. The research investigated JA role on AR-formation and xylogenesis in Arabidopsis dark-grown seedlings and TCLs, and the relationship with ET and auxin. The JA-donor methyl-jasmonate (MeJA), and/or the ET precursor 1-aminocyclopropane-1-carboxylic acid were applied, and the response of mutants in JA-synthesis and -signalling, and ET-signalling investigated. Endogenous levels of auxin, JA and JA-related compounds, and ARF6, ARF8 and ARF17 expression were monitored. Results: MeJA, at 0.01 μM, enhances AR-formation, when combined with IBA + Kin, and the response of the early-JA-biosynthesis mutant dde2–2 and the JA-signalling mutant coi1–16 confirmed this result. JA levels early change during TCL-culture, and JA/JA-Ile is immunolocalized in AR-tips and xylogenic cells. The high AR-response of the late JA-biosynthesis mutant opr3 suggests a positive action also of 12-oxophytodienoic acid on AR-formation. The crosstalk between JA and ET-signalling by EIN3/EIL1 is critical for AR-formation, and involves a competitive modulation of xylogenesis. Xylogenesis is enhanced by a MeJA concentration repressing AR-formation, and is positively related to ARF17 expression. Conclusions: The JA concentration-dependent role on AR-formation and xylogenesis, and the interaction with ET opens the way to applications in the micropropagation of recalcitrant species