Euclidean N=2 supergravity

Euclidean special geometry has recently been investigated in the context of Euclidean supersymmetric theories with vector multiplets. In the rigid case, the scalar manifold is described by affine special para-Kähler geometry while the target geometries of Euclidean vector multiplets coupled to supergravity are given by projective special para-Kähler manifolds. In this Letter, we derive the Killing spinor equations of Euclidean N=2 supergravity theories coupled to vector multiplets. These equations provide the starting point for finding general supersymmetric instanton solutions.