Special Geometry of Euclidean Supersymmetry III: the local r-map, instantons and black holes

Understand

We define and study projective special para-Kahler manifolds and show that they appear as target manifolds when reducing five-dimensional vector multiplets coupled to supergravity with respect to time.

• The dimensional reductions with respect to time and space are carried out in a uniform way using an epsilon-complex notation.
• We explain the relation of our formalism to other formalisms of special geometry used in the literature.
• In the second part of the paper we investigate instanton solutions and their dimensional lifting to black holes.