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We study systematically the conformal geometry of higher spin bosonic gaugefields in three spacetime dimensions. We recall the definition of the Cottontensor for higher spins and establish a number of its properties that turn outto be key in solving in terms of prepotentials the constraint equations of theHamiltonian (3 + 1) formulation of four-dimensional higher spin gauge fields.The prepotentials are shown to exhibit higher spin conformal symmetry. Just asfor spins 1 and 2, they provide a remarkably simple, manifestly dualityinvariant formulation of the theory. While the higher spin conformal geometryis developed for arbitrary bosonic spin, we explicitly perform the Hamiltoniananalysis and derive the solution of the constraints only in the illustrativecase of spin 3. In a separate publication, the Hamiltonian analysis in terms ofprepotentials is extended to all bosonic higher spins using the conformal toolsof this paper, and the same emergence of higher spin conformal symmetry isconfirmed.

Higher Spin Conformal Geometry in Three Dimensions and Prepotentials for Higher Spin Gauge Fields