On hyperbolicity of SU(2)-equivariant, punctured disc bundles over the complex affine quadric

Given a holomorphic line bundle over the complex affine quadric (2), we investigate its Stein, SU(2)-equivariant disc bundles. Up to equivariant biholomorphism, these are all contained in a maximal one, say Omega(max). By removing the zero section from Omega(max) one obtains the unique Stein, SU(2)-equivariant, punctured disc bundle over (2) which contains entire curves. All other such punctured disc bundles are shown to be Kobayashi hyperbolic.