On Quasi-umbilical Locally Strongly Convex Homogeneous Affine Hypersurfaces

In this paper. by developing the techniques of F. Dillen and L. Vrancken in [12], we study quasi-umbilical locally strongly convex homogeneous affine hypersurfaces. We will present a characterization of a special quasi-umbilical affine homogeneous hypersurface for all dimensions, then a complete classification of five-dimensional such hypersurfaces will be given.