Projective Connections and the Algebra of Densities

Details Projective Connections and the Algebra of Densities Projective Connections and the Algebra of Densities

2008-08-20

arxiv.org/abs/0808.2831v1

Mathematics

Differential Geometry

7 pages

Scientific paper

10.1063/1.3043853

Projective connections first appeared in Cartan's papers in the 1920's. Since then they have resurfaced periodically in, for example, integrable systems and perhaps most recently in the context of so called projectively equivariant quantisation. We recall the notion of projective connection and describe its relation with the algebra of densities on a manifold. In particular, we construct a Laplace-type operator on functions using a Thomas projective connection and a symmetric contravariant tensor of rank 2 (`upper metric').

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