Projective Connections and Schwarzian Derivatives for Supermanifolds, and Batalin-Vilkovisky Operators

Details Projective Connections and Schwarzian Derivatives for Supermanifolds, and Batalin-Vilkovisky Operators Projective Connections and Schwarzian Derivatives for Supermanifolds, and Batalin-Vilkovisky Operators

2009-09-29

arxiv.org/abs/0909.5419v1

Mathematics

Differential Geometry

11 pages, no figures

Scientific paper

We extend the notion of a Thomas projective connection (a projective equivalence class of linear connections) for supermanifolds. As a by-product, we arrive at a generalisation of the multidimensional Schwarzian derivative for the super case which was previously unknown. This is combined with our previous construction of a Laplacian on the algebra of densities for a projectively connected manifold and allows us to study Batalin-Vilkovisky type operators and the relation between projective connections and odd Poisson structures.

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