Model-surface method: an infinite-dimensional version
A `model surface' is a homogeneous real-algebraic submanifold of the complex space \(\mathbb C^N\) that strongly osculates a real submanifold of \(\mathbb C^N\). The most common case is a hermitian quadric modelled on the Levi form of a real submanifold in complex space. The geometry of model surfaces is rather transparent and it governs the geometry of more general submanifolds. In particular, the (infinitesimal) automorphisms of a germ of a manifold can be represented as a sub-Lie algebra of the automorphisms of the corresponding model surface. In the paper under review the author generalizes some notions and results on model surfaces to the infinite dimensional case. Most of the facts transfer literally. However non-degenerate Levi-Tanaka algebras now may be of infinite depth.
scientific article; zbMATH DE number 6353214
scientific article