A Canonical Laplacian on the Algebra of Densities on a Projectively Connected Manifold

Jacob George

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arXiv · 0909.5411

A Canonical Laplacian on the Algebra of Densities on a Projectively Connected Manifold

Jacob George

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Abstract

On a manifold with a projective connection we canonically assign a second order differential operator acting on the algebra of all densities to any tensor density $S^{ij}$ of fixed weight $λ$. In particular, this implies that on any projectively connected manifold, a `bracket' (symmetric biderivation) on the algebra of functions extends canonically to the algebra of densities.

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Jacob George. 2009-09-29. A Canonical Laplacian on the Algebra of Densities on a Projectively Connected Manifold. https://arxiv.org/abs/0909.5411

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