On Holomorphic Curves Tangent to Real Hypersurfaces of Infinite Type

Abstract

The purpose of this paper is to investigate the geometric properties of real hypersurfaces of D’Angelo infinite type in $${{\mathbb {C}}}^n$$ C n . In order to understand the situation of flatness of these hypersurfaces, it is natural to ask whether there exists a nonconstant holomorphic curve tangent to a given hypersurface to infinite order. A sufficient condition for this existence is given by using Newton polyhedra, which is an important concept in singularity theory. More precisely, equivalence conditions are given in the case of some model hypersurfaces.