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Metrisability of three-dimensional path geometries

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Publication Date: 2016-03-08

Journal Title: European Journal of Mathematics

Publisher: Springer

Volume: 2

Issue: 3

Pages: 809-834

Language: English

Type: Article

This Version: AM

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Citation: Dunajski, M., & Eastwood, M. (2016). Metrisability of three-dimensional path geometries. European Journal of Mathematics, 2 (3), 809-834.

Description: This is the author accepted manuscript. The final version is available from Springer via

Abstract: Given a projective structure on a three-dimensional manifold, we find explicit obstructions to the local existence of a Levi-Civita connection in the projective class. These obstructions are given by projectively invariant tensors algebraically constructed from the projective Weyl curvature. We show, by examples, that their vanishing is necessary but not sufficient for local metrisability.

Keywords: projective differential geometry, path geometry, Weyl geometry, metrisability

Sponsorship: Science and Technology Facilities Council


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Author: Dunajski, MaciejEastwood, Michael



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