In this paper, we study locally strongly convex Tchebychev hypersurfaces, namely the {\it centroaffine totally umbilical hypersurfaces}, in $(n+1)$-dimensional affine space $\mathbb{R}^{n+1}$. We first make an ordinary-looking observation that such hypersurfaces are characterized by having a Riemannian structure admitting canonically defined closed conformal vector field. Then, taking advantage...
