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
Metadata: Show full item record
Citation: Dunajski, M., & Eastwood, M. (2016). Metrisability of three-dimensional path geometries. European Journal of Mathematics, 2 (3), 809-834. https://doi.org/10.1007/s40879-016-0095-3
Description: This is the author accepted manuscript. The final version is available from Springer via http://dx.doi.org/10.1007/s40879-016-0095-3
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
Identifiers:
External DOI: https://doi.org/10.1007/s40879-016-0095-3
This record's URL: https://www.repository.cam.ac.uk/handle/1810/260105
Autor: Dunajski, MaciejEastwood, Michael
Fuente: https://www.repository.cam.ac.uk/handle/1810/260105