On the automorphism group of a complex sphere

Abstract

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 [HKP] and [CDP] the dimension of $Aut(X)$ is at most 2. We prove that $Aut(X)$ cannot be isomorphic to the complex affine group.