Linear Weingraten factorable surfaces in isotropic spaces

TL;DR

This paper classifies linear Weingarten factorable surfaces in isotropic 3-space, focusing on those satisfying specific curvature relations, and explores surfaces satisfying the Euler inequality equality in this geometric context.

Contribution

It provides a complete classification of such surfaces in isotropic space and analyzes surfaces meeting the K=H^2 condition, extending curvature theory in isotropic geometry.

Findings

Complete classification of linear Weingarten factorable surfaces in I^3.

Identification of surfaces satisfying K=H^2 in isotropic space.

Extension of curvature relations to isotropic geometric settings.

Abstract

In this paper, we deal with the linear Weingarten factorable surfaces in the isotropic 3-space I^{3} satisfying the relation aK+bH=c, where K is the relative curvature and H the isotropic mean curvature, a,b,cR. We obtain a complete classification for such surfaces in I^{3}. As a further study, we classify all graph surfaces in I^{3} satisfying the relation K=H^{2}, which is the equality case of the famous Euler inequality for surfaces in a Euclidean space.