  We show that in special K\"ahler geometry of $N=2$ space-time supergravity
the gauge variant part of the connection is holomorphic and flat (in a
Riemannian sense). A set of differential identities (Picard-Fuchs identities)
are satisfied on a holomorphic bundle. The relationship with the differential
equations obeyed by the periods of the holomorphic three form of Calabi-Yau
manifolds is outlined.
