Rotational Surfaces in Isotropic Spaces Satisfiying Weingarten Conditions

TL;DR

This paper classifies rotational surfaces in isotropic 3-space that satisfy specific Weingarten conditions relating their relative curvature and isotropic mean curvature, expanding understanding of their geometric properties.

Contribution

It provides a classification of linear Weingarten rotational surfaces in isotropic 3-space, a novel contribution to the geometry of isotropic spaces.

Findings

Classification of linear Weingarten rotational surfaces in I^3

Explicit descriptions of surfaces satisfying curvature relations

Extension of classical surface theory to isotropic geometry

Abstract

In this paper, we study the rotational surfaces in the isotropic 3-space I^3. satisfying Weingarten conditions in terms of the relative curvature K (analogue of the Gaussian curvature) and the isotropic mean curvature H. In particular, we classify such surfaces of linear Weingarten type in I^3.