Projective Connections and the Algebra of Densities

Jacob George

doi:10.1063/1.3043853

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arXiv · 0808.2831

Projective Connections and the Algebra of Densities

Jacob George

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Abstract

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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Jacob George. 2008-08-20. Projective Connections and the Algebra of Densities. https://doi.org/10.1063/1.3043853

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