Schwartz, Philip and Read, James and Vigneron, Quentin (2026) Weyl-type theorems in Galilei and Carroll geometry. [Preprint]

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Abstract

A classic theorem of Weyl (1921) states that a Weyl metric---a natural generalisation of a pseudo-Riemannian metric---is uniquely determined by its conformal and projective structures (i.e. by its conformal structure and its set of unparametrised geodesics). An equivalent formulation of Weyl's result is that a torsion-free linear connection compatible with a pseudo-Riemannian conformal structure is uniquely determined by its projective structure. We discuss analogous results for suitably defined notions of conformal structure for Galilei and Carroll geometry, i.e. for spacetime geometries arising as the 'non-relativistic' and 'ultra-relativistic' limits of Lorentzian geometry.

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Item Type:	Preprint
Creators:	Creators Email ORCID Schwartz, Philip philip.schwartz@itp.uni-hannover.de Read, James james.read@philosophy.ox.ac.uk Vigneron, Quentin quentin.vigneron@umk.pl
Keywords:	Weyl's theorem, projective structure, conformal structure, Galilean gravity, Carroll gravity
Subjects:	Specific Sciences > Physics > Classical Physics Specific Sciences > Physics > Relativity Theory
Depositing User:	Dr. James Read
Date Deposited:	31 May 2026 12:47
Last Modified:	31 May 2026 12:47
Item ID:	29833
Subjects:	Specific Sciences > Physics > Classical Physics Specific Sciences > Physics > Relativity Theory
Date:	30 May 2026
URI:	https://philsci-archive.pitt.edu/id/eprint/29833

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