Conformal Schwarzian derivatives and conformally invariant quantization

Details Conformal Schwarzian derivatives and conformally invariant quantization Conformal Schwarzian derivatives and conformally invariant quantization

2001-10-31

arxiv.org/abs/math/0110337v2

International Math. Res. Not. 2002, no. 29, 1553-1570

Mathematics

Differential Geometry

15 pages, Latex2e, major corrections, to appear in Int. Math. Res. Not

Scientific paper

Let $(M,g)$ be a pseudo-Riemannian manifold. We propose a new approach for defining the conformal Schwarzian derivatives. These derivatives are 1-cocycles on the group of diffeomorphisms of $M$ related to the modules of linear differential operators. As operators, these derivatives do not depend on the rescaling of the metric $g.$ In particular, if the manifold $(M,g)$ is conformally flat, these derivatives vanish on the conformal group $\Og(p+1,q+1),$ where $\mathrm{dim} (M)=p+q.$ This work is a continuation of [1,4] where the Schwarzian derivative was defined on a manifold endowed with a projective connection.

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