Centroaffine Translation Surfaces in R3

The centroaffine theorema egregium chi = J - n/n-1G(T,T) + 1 is a fundamental scalar identity in the centroaffine differential geometry for non-degenerate hypersurface immersions. Here n is the dimension of the hypersurface, chi the normalized scalar curvature of the centroaffine metric G, J the Pick invariant and T the centroaffine Tchebychev vector field. In this paper we study non-degenerate centroaffine translation surfaces in affine 3-space R-3 where one of the three summands in the centroaffine theorema egregium is constant, and then give the classifications by solving certain partial differential equations.