On the affine connections that give rise to a given curvature

Summary A problem of both theoretical and practical importance is that of characterizing the collection of all affine connections that gives rise to a given curvature structure on a subset of a differentiable manifold of finite dimension. This problem is solved in closed form in Section three. We also show that the cardinality of the collection of all distinct connections that give the same curvature is that of the continuum, and that the connections of any two curvature structures can be brought into a1-to-1 correspondence. Entrata in Redazione il 2 dicembre 1976.     

Ruled Special Lagrangian 3-Folds In C3

This is the fifth in a series of papers constructing explicitexamples of special Lagrangian submanifolds in C^m. A submanifoldof C^m is ruled if it is fibred by a family of real straightlines in C^m. This paper studies ruled special Lagrangian 3-foldsin C³, giving both general theory and families of examples.Our results are related to previous work of Harvey and Lawson,Borisenko, and Bryant. Special Lagrangian cones in C³ are automaticallyruled, and each ruled special Lagrangian 3-fold is asymptoticto a unique special Lagrangian cone. We study the family ofruled special Lagrangian 3-folds N asymptotic to a fixed specialLagrangian cone N0. We find that this depends on solving a linearequation, so that the family of such N has the structure ofa vector space. We also show that the intersection of N0 withthe unit sphere S⁵ in C³ is a Riemann surface, and constructa ruled special Lagrangian 3-fold N asymptotic to N0 for eachholomorphic vector field w on . As corollaries of this we writedown two large families of explicit special Lagrangian 3-foldsin C³ depending on a holomorphic function on C, which includemany new examples of singularities of special Lagrangian 3-folds.We also show that each special Lagrangian T2-cone N0 can beextended to a 2-parameter family of ruled special Lagrangian3-folds asymptotic to N0, and diffeomorphic to T²xR. 2000 Mathematical Subject Classification: 53C38, 53D12.     

A comparison of predicted and experimental vibrational spectra in some small fluorocarbons

The vibrational assignments of difluoromethane, cis and trans 1,2-difluoroethylene, trifluoroethylene, 2-fluoropropene, 1,1-difluoroethylene, and tetrafluoroethylene have been reassessed in the light of recent theoretical work. Inconsistent experimental wave number values and assignments have been clarified, and some changes to the experimental assignments are proposed. The assignments compare favorably with recent scaled density functional theory calculations using the hybrid three-parameter B3-PW91 density functional.     

The total synthesis of the annonaceous acetogenin, muricatetrocin C

The total synthesis of the potential antitumour agent muricatetrocin C has provided an ideal stage for the exploitation and development of new chemistry. A convergent synthetic strategy has been realised incorporating three distinct pieces of methodology, these include a highly diastereoselective hetero-Diels-Alder reaction to construct the butenolide terminus, an oxygen to carbon rearrangement to install the trans-2,5-disubstituted tetrahydrofuran ring and a spatial desymmetrisation process to afford the anti-diol unit.     

Cage compounds of heterotrimetallic mixed phosphanediide/silanolate aggregates with an alkaline Earth metal-centered phosphorus octahedron

The lithiation of potassium triisopropylsilylphosphanide yields the corresponding phosphanediide. The subsequent metathesis reaction with SrI(2) and BaI(2) in the presence of hexamethyldisiloxane gives hexalithium hexapotassium strontium hexakis(triisopropylsilylphosphanediide)bis(trimethylsilanolate) (1) and the corresponding barium derivative (2), respectively. The alkaline earth metal atoms are surrounded octahedrally by the phosphanediide ligands. Six P(3) faces of the octahedron are capped by the K atoms, and the P-P edges of two opposite P(3) faces are bridged by the lithium atoms. The Li cations are also bonded to the Me(3)SiO substituents giving a coordination number of three for the alkali metals.     

Kinetics of reductive N-O bond fragmentation: the role of a conical intersection

N-alkoxyheterocycles can act as powerful one-electron acceptors in photochemical electron-transfer reactions. One-electron reduction of these species results in formation of a radical that undergoes N-O bond fragmentation to form an alkoxy radical and a neutral heterocycle. The kinetics of this N-O bond fragmentation reaction have been determined for a series of radicals with varying substituents and extents of delocalization. Rate constants varying over 7 orders of magnitude are obtained. A reaction potential energy surface is described that involves avoidance of a conical intersection. A molecular basis for the variation of the reaction rate constant with radical structure is given in terms of the relationship between the energies of the important molecular orbitals and the reaction potential energy surface. Ab initio and density functional electronic structure calculations provide support for the proposed reaction energy surface.     

Quasi-ALE Metrics with Holonomy SU(m) and Sp(m)

Let G be a finite subgroup of U(m),and X a resolution of ^m /G. We define aspecial class of Kähler metrics g on Xcalled Quasi Asymptotically Locally Euclidean (QALE) metrics. Thesesatisfy a complicated asymptotic condition, implying that gis asymptotic to the Euclidean metric on ^m /G away fromits singular set. When ^m /Ghas an isolated singularity,QALE metrics are just ALE metrics. Our main result is an existencetheorem for Ricci-flat QALE Kähler metrics: if G is afinite subgroup of SU(m) and X a crepant resolution of ^m /G, then there is a unique Ricci-flat QALE Kähler metric on X in each Kähler class.This is proved using a version of the Calabi conjecture for QALEmanifolds. We also determine the holonomy group of the metrics in termsof G.     

The first example of a Si-bridged tris(pyridyl) ligand; synthesis and structure of [MeSi(2-C5H4N)3LiX](X = 0.2Br, 0.8Cl)

The low-temperature reaction of MeSiCl3 with 2-Li-C5H4N (1:3 equivalents) in thf gives [MeSi(2-C5H4N)3LiX](X = 0.2Br, 0.8Cl), containing the first example of a Si-bridged tris(pyridyl) ligand.