Proper actions of Lie groups of dimension \(n^{2} + 1\) on \(n\)-dimensional complex manifolds
The authors continue a study of actions of high-dimensional Lie groups on complex manifolds. They give explicit description of all pairs \((M,G)\), where \(M\) is a connected complex manifold of dimension \(n\geq 2\) and \(G\) is a connected Lie group of dimension \(n^2+1\) acting effectively and properly on \(M\) by holomorphic transformations. The result complements a classification obtained earlier by the first author for \(n^2+2\leq\dim\;G<n^2+2n\) and a classical result due to W. Kaup for the maximal group dimension \(n^2+2n\).
scientific article; zbMATH DE number 5610605
scientific article