Classification of homothetical hypersurfaces and its applications to production functions in economics

TL;DR

This paper classifies a specific type of hypersurfaces with zero curvature in Euclidean space and explores their applications to economic production functions.

Contribution

It provides a complete classification of homothetical hypersurfaces with null Gauss-Kronocker curvature and applies these results to economic models.

Findings

Classified all homothetical hypersurfaces with null Gauss-Kronocker curvature.

Established connections between geometric hypersurfaces and economic production functions.

Provided new insights into the geometric structure of production functions in economics.

Abstract

In this paper, we completely classify the homothetical hypersurfaces having null Gauss-Kronocker curvature in a Euclidean (n+1)-space. Several applications to the production functions in economics are also given.