Geometry of Centroaffine Surfaces in $\mathbb{R}^5$

TL;DR

This paper employs Cartan's moving frames to derive local invariants and classify all homogeneous nondegenerate centroaffine surfaces in five-dimensional space, advancing the understanding of their geometric structure.

Contribution

It provides a complete set of invariants and a classification of homogeneous centroaffine surfaces in ive-dimensional space, a novel extension in affine differential geometry.

Findings

Derived a full set of local invariants for the surfaces.

Classified all homogeneous centroaffine surfaces in ive-dimensional space.

Abstract

We use Cartan's method of moving frames to compute a complete set of local invariants for nondegenerate, 2-dimensional centroaffine surfaces in $\mathbb{R}^5 \setminus \{0\}$ with nondegenerate centroaffine metric. We then give a complete classification of all homogeneous centroaffine surfaces in this class.