Proper actions of lie groups of dimension n ² + 1 on n-dimensional complex manifolds

In this paper, we continue to study actions of high-dimensional Lie groups on complex manifolds. We give a complete explicit description of all pairs (M,G), where M is a connected complex manifold of dimension n ≥ 2 and G is a connected Lie group of dimension n² +1 acting effectively and properly on M by holomorphic transformations. This result complements a classification obtained earlier by the first author for n² + ² ≤ dimG < n² + 2n and a classical result due to W. Kaup for the maximal group dimension n² + 2n.