  A production function $f$ is called quasi-sum if there are strict monotone
functions $F, h_1,...,h_n$ with $F'>0$ such that $$f(x)= F(h_1 (x_1)+...+h_n
(x_n)).$$ The justification for studying quasi-sum production functions is that
these functions appear as solutions of the general bisymmetry equation and they
are related to the problem of consistent aggregation.
  In this article, first we present the classification of quasi-sum production
functions satisfying the constant elasticity of substitution property. Then we
prove that if a quasi-sum production function satisfies the constant elasticity
of substitution property, then its graph has vanishing Gauss-Kronecker
curvature (or its graph is a flat space) if and only if the production function
is either a linearly homogeneous generalized ACMS function or a linearly
homogeneous generalized Cobb-Douglas function.
