On the real-analytic infinitesimal CR automorphism of hypersurfaces of infinite type

TL;DR

This paper investigates the structure of infinitesimal CR automorphisms of real hypersurfaces of infinite type in complex two-space, showing they are either trivial or one-dimensional.

Contribution

It establishes a precise classification of the space of tangential holomorphic vector fields at points of infinite type hypersurfaces in ^2.

Findings

The space of such vector fields is either trivial or one-dimensional.

Provides a classification result for infinite type hypersurfaces.

Clarifies the structure of automorphisms at infinite type points.

Abstract

In this article, we consider a real smooth hypersurface $M\subset \mathbb C^2$, which is of infinite type at $p\in M$. The purpose of this paper is to show that the real vector space of tangential holomorphic vector field germs at $p$ vanishing at $p$ is either trivial or of real dimension $1$.