Real Submanifolds of Codimension Two in Complex Manifolds

Abstract

The equivalence problem for a real submanifold $M$ of dimension at least eight and codimension two in a complex manifold is solved under a certain nondegeneracy condition on the Levi form. If the Levi forms at all points of $M$ are equivalent, a normalized Cartan connection can be defined on a certain principal bundle over $M$. The group of this bundle can be described by means of the osculating quartic of $M$ or the prolongation of the graded Lie algebra of type ${\mathfrak {g}_2} \oplus {\mathfrak {g}_1}$ defined by the Levi form.