10D to 4D Euclidean supergravity over a Calabi-Yau three-fold

We dimensionally reduce the bosonic sector of 10D Euclidean type IIA supergravity over a Calabi-Yau three-fold. The resulting theory describes the bosonic sector of 4D, $N=2$ Euclidean supergravity coupled to vector- and hyper-multiplets. We show that the scalar target manifold of the vector-multiplets is projective special para-Kähler, and is therefore of split signature, whereas the target manifold of the hyper-multiplets is (positive-definite) quaternionic Kähler. (paper)