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arXiv · 2501.07460

Weyl metrizability of 3-dimensional projective structures and CR submanifolds

Omid Makhmali
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Abstract

A projective structure is Weyl metrizable if it has a representative that preserves a conformal structure. We interpret Weyl metrizability of 3-dimensional projective structures as certain 5-dimensional nondegenerate CR submanifolds in a class of 7-dimensional 2-nondegenerate CR structures. As a corollary, it follows that in dimension three Beltrami's theorem extends to conformal structures, i.e. a locally flat projective structure is Weyl metrizable exclusively with respect to a locally flat conformal structure. In higher dimensions it is shown that conformal Beltrami theorem remains true as well.

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Omid Makhmali. 2025-01-13. Weyl metrizability of 3-dimensional projective structures and CR submanifolds. https://doi.org/10.1007/s00209-026-03958-0

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