2025/01/13 by Makhmali, Omid
#32V05 #32V40 #53A55 #53C05 #53C18 #53C28 #Differential Geometry (math.DG) #FOS: Mathematics #Primary: 53A20 #Secondary: 53C24
paper · doi:10.48550/arxiv.2501.07460
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 flat projective structure is Weyl metrizable exclusively with respect to a flat conformal structure. In higher dimensions it is shown that conformal Beltrami theorem remains true as well.