On the automorphism group of a complex sphere (Q1305175)

Summary: Let \(X\) be a compact complex threefold with the integral homology of \({\mathbf S}^6\) and let \(\Aut(X)\) be its holomorphic automorphism group. By \textit{A. Huckleberry, S. Kebekus} and \textit{T. Peternell} [Group actions on \({\mathbf S}^6\) and complex structure on \({\mathbf P}^3\), preprint math. AG/9812076 (1998)] and \textit{F. Campana, J.-P. Demailly} and \textit{T. Peternell} [Compos. Math. 112, No. 1, 77-91 (1998; Zbl 0910.32032)] the dimension of \(\Aut(X)\) is at most 2. We prove that \(\Aut(X)\) cannot be isomorphic to the complex affine group.