  Given a holomorphic Lagrangian fibration of a compact hyperkahler manifold,
we use the differential geometry of the special Kahler metric that exists on
the base away from the discriminant locus, and show that the pullback of the
tangent bundle of the base to the total space of a family of minimal rational
curves admits a parallel splitting. The splitting is nontrivial when the base
is not half-dimensional projective space. Combining this with results of
Voisin, Hwang and Bakker-Schnell, we deduce that the base must be projective
space, a result first proved by Hwang.
