Special metrics and scales in parabolic geometry

Annals of Global Analysis and Geometry - Given a parabolic geometry, it is sometimes possible to find special metrics characterised by some invariant conditions. In conformal geometry, for example,...     

Convergent synthesis of a complex oxime library using chemical domain shuffling

[reaction: see text] The synthesis of a complex hybrid oxime library is reported utilizing convergent ligation of alkoxyamine and carbonyl monomers via "chemical domain shuffling". Initial biological screening of the library against human small cell lung carcinoma (A549) cells led to the identification of a novel hybrid dimer in contrast to the corresponding monomeric compounds which were found to be inactive.     

Local Constraints on Einstein–Weyl Geometries: The 3-Dimensional Case

Following an earlier study [3], we consider the Einstein–Weyl equations on a fixed (complex) background metric as an equation for a 1-form and its first few derivatives. If the background is flat then we conclude that the only solutions are conformal rescalings of constant curvature metrics. If the background is a homogeneous 3-geometry in Bianchi class A (i.e., with unimodular isometry group), we find necessary and sufficient conditions on the 3-geometry for solutions of the Einstein–Weyl equations to exist. The solutions we find are complexifications of known ones. In particular, we find that the general left-invariant metric on S³ and the metric 'Sol' admit no local solutions of the Einstein–Weyl equations.