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

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.