2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/108763We review recent developments in special geometry, emphasizing the role of real coordinates. In the first part we discuss the para-complex geometry of vector and hypermultiplets in rigid Euclidean N=2 supersymmetry. In the second part we study the variational principle governing the near horizon limit of BPS black holes in matter-coupled N=2 supergravity and observe that the black hole entropy is the Legendre transform of the Hesse potential encoding the geometry of the scalar fields.27 pages, contributed to the Handbook on Pseudo-Riemannian Geometry and SupersymmetryHigh Energy Physics - Theorytext