The purpose of this paper is to investigate the geometric properties of real hypersurfaces of D’Angelo infinite type in \({{\mathbb {C}}}^n\). 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.

中文翻译：

---

与无限大的实超曲面相切的全纯曲线

本文的目的是研究\（{{\ mathbb {C}}} ^ n \）中D'Angelo无限类型的实超曲面的几何性质。为了理解这些超曲面的平整度的情况，很自然地要问是否存在与给定超曲面相切的无限等阶全纯曲线。通过使用牛顿多面体给出了存在的充分条件，牛顿多面体是奇异性理论中的一个重要概念。更确切地说，在某些模型超曲面的情况下给出了等效条件。