Three dimensional locally homogeneous nondegenerate centroaffine hypersurfaces with null Tchebychev vector field

Abstract

Liu and Wang (Beitrage Algebra Geom 35:109–117, 1994) determined homogeneous nondegenerate centroaffine surfaces in the 3-dimensional affine space. However, n-dimensional homogeneous or locally homogeneous nondegenerate centroaffine hypersurfaces for \(n\ge 3\) have not been completely classified yet. In this paper,we determine 3-dimensional locally homogeneous nondegenerate centroaffine hypersurfaces with null Tchebychev vector field.