Projection on Segre varieties and determination of holomorphic mappings between real submanifolds

It is shown that a germ of a holomorphic mapping sending a real-analytic generic submanifold of finite type into another is determined by its projection on the Segre variety of the target manifold. A necessary and sufficient condition is given for a germ of a mapping into the Segre variety of the target manifold to be the projection of a holomorphic mapping sending the source manifold into the target. An application to the biholomorphic equivalence problem is also given.Comment: 16 page

Proper Actions of Lie Groups of Dimension n2 + 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 di

Effective actions of the unitary group on complex manifolds

We classify all connected n-dimensional complex manifolds admitting effective actions of the unitary group Un by biholomorphic transformations. One consequence of this classification is a characterization of ℂn by its automorphism group