A short proof of the Dimension Conjecture for real hypersurfaces in ${\mathbb C}^2$

TL;DR

This paper presents a concise proof of the Dimension Conjecture for real hypersurfaces in complex two-dimensional space, which characterizes spherical hypersurfaces through automorphism algebra dimensions.

Contribution

It offers a shorter, more efficient proof of the previously established Dimension Conjecture for ${f C}^2$ hypersurfaces.

Findings

Confirmed the Dimension Conjecture with a simplified proof

Characterized spherical hypersurfaces via automorphism algebra dimensions

Provided a new approach to understanding hypersurface automorphisms

Abstract

Recently, I. Kossovskiy and R. Shafikov have settled the so-called Dimension Conjecture, which characterizes spherical hypersurfaces in ${\mathbb C}^2$ via the dimension of the algebra of infinitesimal automorphisms. In this note, we propose a short argument for obtaining their result.