Real Abelian varieties with many line bundles

Let X and Y be affine nonsingular real algebraic varieties. A general problem in real algebraic geometry is to try to decide when a continuous map f : X --> Y can be approximated by regular maps in the space of Y-0 mappings from X to Y, equipped with the Y-0 topology-This paper solves this problem when X is the connected component containing the origin of the real part of a complex Abelian variety and Y is the standard 2-dimensional sphere.