A Berger-type theorem for metric connections with skew-symmetric torsion

We prove a Berger-type theorem which asserts that if the orthogonal subgroup generated by the torsion tensor (pulled back to a point by parallel transport) of a metric connection with skew-symmetric torsion is not transitive on the sphere, then the space must be locally isometric to a Lie group with a bi-invariant metric or its symmetric dual (we assume the space to be locally irreducible). We also prove that a (simple) Lie group with a bi-invariant metric admits only two flat metric connections with skew-symmetric torsion: the two flat canonical connections. In particular, we get a refinement of a well-known theorem by Cartan and Schouten. Finally, we show that the holonomy group of a metric connection with skew-symmetric torsion on these spaces generically coincides with the Riemannian holonomy.Comment: 13 pages; we add some new examples and fix minor misprints; final version to appear in Journal of Geometry and Physic

The isotropy lattice of a lifted action

We obtain an algorithmic construction of the isotropy lattice for a lifted action of a Lie group $G$ on $TM$ and $T^*M$ based only on the knowledge of $G$ and its action on $M$. Some applications to symplectic geometry are also shown.Comment: minor modification

Definition of a Balancing Point for Electricity Transmission Contracts

Electricity transmission contracts allocate scarce resources, allow hedging against locational price differences and provide information to guide investment. Liquidity is increased if all transmission contracts are defined relative to one balancing point, then a set of two contracts can replicate any point to point contract. We propose an algorithm and apply it to the European electricity network to identify a well connected balancing point that exhibits minimal relative cross-price responses and hence reduces market power exercised by generation companies. Market level data which is difficult to obtain or model such as price levels in different regions or that is dependent on the time scale of interaction, as demand elasticity, is not required. The only critical input quantities are assumptions on future transmission constraint patterns

Rydberg rings

Atoms in highly excited Rydberg states exhibit remarkable properties and constitute a powerful tool for studying quantum phenomena in strongly interacting many-particle systems. We investigate alkali atoms that are held in a ring lattice and excited to Rydberg states. The system constitutes an ideal model system to study thermalization of a coherently evolving quantum many-particle system in the absence of a thermal bath. Moreover, it offers exciting perspective to create entangled many-body quantum states which can serve as a resource for the generation of single photons.Comment: invited PCCP Perspectiv

A note on the uniqueness of the canonical connection of a naturally reductive space

We extend the result in J. Reine Angew. Math. 664, 29-53, to the non-compact case. Namely, we prove that the canonical connection on a simply connected and irreducible naturally reductive space is unique, provided the space is not a sphere, a compact Lie group with a bi-invariant metric or its symmetric dual. In particular, the canonical connection is unique for the hyperbolic space when the dimension is different from three. We also prove that the canonical connection on the sphere is unique for the symmetric presentation. Finally, we compute the full isometry group (connected component) of a compact and locally irreducible naturally reductive space.Comment: 7 page

Europe and the EU: IRS contribution for the 2003 Organic Food and Farming Report

Organic and in-conversion land area in the EU-15 has grown in 2002 to approximately 5.1m hectares and 3.6 per cent of utilisable agricultural area on 165,500 holdings. In this period land area grew by an estimated 10 per cent with increases in the number of farms at 6 per cent. The EU Commission has recognised the importance of organic farming in encouraging more environmentally farming methods has taken further steps to improve policy support. A consultation for the development of an EU Action Plan for organic farming took place during 2002 and the publication of further steps is expected at the end of 2003. These developments were in some way driven by a high profile policy conference organised by the Danish Government in May 2001. Other EU policy developments are likely to include the facilitation of sales, closer targeting of organic farming to Environmentally Sensitive Areas, measures to encourage the exchange of technical information and the traceability and authenticity of organic food. Some small changes have also come into force in the EU Regulation 2092/91: the Annex III on inspection regimes was updated in December 2001, and other Annexes were amended including some minor changes to the list of approved pesticides