Polynomial Translation Weingarten Surfaces in 3-dimensional Euclidean space

TL;DR

This paper classifies polynomial translation surfaces in 3D Euclidean space that are Weingarten surfaces, focusing on those satisfying specific curvature relations and exploring surfaces with power functions where the second Gaussian curvature is zero.

Contribution

It provides a classification of polynomial translation Weingarten surfaces and examines surfaces with power functions with zero second Gaussian curvature.

Findings

Classification of polynomial translation Weingarten surfaces.

Analysis of surfaces satisfying 2aH + bK = 0.

Study of translation surfaces with power functions and zero second Gaussian curvature.

Abstract

In this paper we will classify those translation surfaces in E3 involving polynomials which are Weingarten surfaces. We analyze Weingarten translation surfaces satisfying 2aH + bK = 0. We study also other types of translation surfaces, involving power functions, for which the second Gaussian curvature vanishes.