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We construct two new versions of the c-map which allow us to obtain thetarget manifolds of hypermultiplets in Euclidean theories with rigid N =2supersymmetry. While the Minkowskian para-c-map is obtained by dimensionalreduction of the Minkowskian vector multiplet lagrangian over time, theEuclidean para-c-map corresponds to the dimensional reduction of the Euclideanvector multiplet lagrangian. In both cases the resulting hypermultiplet targetspaces are para-hyper-Kahler manifolds. We review and prove the relevantresults of para-complex and para-hypercomplex geometry. In particular, we givea second, purely geometrical construction of both c-maps, by proving that thecotangent bundle N=T^*M of any affine special (para-)Kahler manifold M ispara-hyper-Kahler.Comment: 36 pages, 1 figur

Special geometry of euclidean supersymmetry II. Hypermultiplets and thec-map