摘要：This paper is a new onset about production functions. Because all papers on this subject use the projections of production functions on a plan, the analysis becomes heavy and less general in conclusions, and for this reason we made a treatment from the point of view of differential geometry in space. On the other hand, we generalize the Cobb -Douglas, CES and Sato production functions to a unique form and we made the analysis on this. The conclusions of the paper allude to the principal directions of the surface (represented by the graph of the production function) i.e. the directions in which the function varies the best. Also the concept of the total curvature of a surface is applied here and we obtain that it is null in every point, that is all points are parabolic. We compute also the surface element which is useful to finding all product ion (by means the integral) when both labour and capital are variable
