TRANSLATION HYPERSURFACES AND TZITZEICA TRANSLATION HYPERSURFACES OF THE EUCLIDEAN SPACE

Abstract

The determinants of bordered Hessian matrices (also called Allen's matrices) play important roles in many areas of mathematics and economics. In the present paper, we completely classify the translation hypersurfaces (M-1, f) whose Allen's matrices off are singular in the Euclidean (n+1)-space Rn+1. Also, we obtain that the translation hypersurfaces satisfying the Tzitzeica condition are only hyperplanes in Rn+1. An application of such hypersurfaces to production functions in microeconomics is given.