$$\mathcal{N} = 2$$ Supergravity and Harmonic Superspace: Linearized Supercurvatures

Using the formulation of $$\mathcal{N} = 2$$ supergravity in harmonic superspace, we construct a complete set of linearized supercurvatures that are $$\mathcal{N} = 2$$ supersymmetrizations of the scalar curvature, the irreducible part of the Ricci tensor and the self-dual Weyl tensor. Based on these supercurvatures, the total set of quadratic invariants of the linearized $$\mathcal{N} = 2$$ supergravity is constructed. Supercurvaturies have a beautiful geometric structure and admit a generalization to higher spins, thereby opening the way towards the construction of a number of $$\mathcal{N} = 2$$ supersymmetric cubic interactions of such spins.