A certain class of surfaces on product time scales with interpretations from economics

Abstract

In this study, we consider a graph surface associated to Cobb-Douglas production function in economics on product time scales. We classify this surface based on the flatness and minimality properties for several product time scales. Then, we interpret the obtained results from the perspective of production theory in economics. Therefore, we extend the known results in Euclidean geometry by considering time scale calculus.

Darboux curves on product time scales

“…Then, he extended well-known notions of discrete pseudospherical surfaces and smooth pseudospherical surfaces on more exotic domains. In 2010, Bohner and Guseinov 6 studied surfaces parametrized by time scale parameters and constructed an integral formula to compute area of surfaces on T. In fact, the main purpose of these studies is to unify the difference and differential geometries and to formulate the integrable geometry on T. The number of studies about the applications of differential geometry on T is gradually increasing (see literature [7][8][9][10][11][12][13][14] ).…”

“…In fact, the main purpose of these studies is to unify the difference and differential geometries and to formulate the integrable geometry on . The number of studies about the applications of differential geometry on is gradually increasing (see literature 7–14 ).…”