# Classification of the locally strongly convex centroaffine hypersurfaces with parallel cubic form

## TL;DR

This paper provides a complete classification of locally strongly convex centroaffine hypersurfaces with parallel cubic form, extending previous results in affine differential geometry.

## Contribution

It offers a comprehensive classification of these hypersurfaces, filling a gap in the understanding of centroaffine geometry with parallel cubic forms.

## Key findings

- Complete classification of the hypersurfaces
- Extension of previous affine classification results
- New insights into centroaffine hypersurface geometry

## Abstract

In this paper, we study locally strongly convex centroaffine hypersurfaces with parallel cubic form with respect to the Levi-Civita connection of the centroaffine metric. As the main result, we obtain a complete classification of such centroaffine hypersurfaces. The result of this paper is a centroaffine version of the complete classification of locally strongly convex equiaffine hypersurfaces with parallel cubic form due to Hu, Li and Vrancken [12].