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

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

2011-04-15

arxiv.org/abs/1104.3004v2

Mathematics

Complex Variables

15 pages, v2: minor changes, to appear in Transformation Groups

Scientific paper

10.1007/s00031-011-9167-0

Given a holomorphic line bundle over the complex affine quadric $Q^2$, 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 to $\Omega_{max}$ one obtains the unique Stein, SU(2)-equivariant, punctured disc bundle over $Q^2$ which contains entire curves. All other such punctured disc bundles are shown to be Kobayashi hyperbolic.

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