On Complex Points of Codimension 2 Submanifolds

Abstract

In this paper we study the structure of complex points of codimension 2 real submanifolds in complex $$n$$ -dimensional manifolds. We show that the local structure of complex points up to isotopy only depends on their type (either elliptic or hyperbolic). We also show that any such submanifold can be smoothly isotoped into a submanifold that has 2-strictly pseudoconvex neighborhood basis.