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Employing the same technique as in our previous papers, we establish an intrinsic characterization of the direct product of a complex Euclidean ball and punctured planes in the category of Stein manifolds from the viewpoint of holomorphic automorphism group.

Let M be a connected Stein manifold of dimension n. We show that if the holomorphic automorphism group of M is isomorphic to the holomorphic automorphism group of B-k x Cn-k as topological group, then M itself is biholomorphically equivalent to B-k x Cn-k, where B-k denotes the open unit ball in C-k.

We will prove that the automorphism groups of the strongly pseudoconvex model domains in almost complex manifolds are isomorphically embedded into the automorphism group of the unit ball. (C) 2014 Elsevier Inc. All rights reserved.