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Consider a Hodge manifold and assume that a torus acts on it in a Hamiltonianand holomorphic manner and that this action linearizes on a given quantizingline bundle. Inside the dual of the line bundle one can define the circlebundle, which is a strictly pseudoconvex CR manifold. Then, there is anassociated unitary representation on the Hardy space of the circle bundle.Under suitable assumptions on the moment map, we consider certain loci in unitcircle bundle, naturally associated to a ray through an irreducible weight.Their quotients are called conic transforms. We introduce maps which areasymptotic embeddings of conic transforms making use of the correspondingequivariant Szeg\H{o} projector.

Remarks on asymptotic isometric embeddings of conic transforms for torus actions