Certain classifications on surfaces of revolution in a semi-isotropic space

TL;DR

This paper characterizes surfaces of revolution in semi-isotropic space that satisfy specific differential equations involving the Laplace operator, expanding understanding of geometric properties in this non-Euclidean setting.

Contribution

It provides a detailed description of surfaces of revolution in semi-isotropic space satisfying certain Laplace equations, a novel exploration in this geometric context.

Findings

Classification of revolution surfaces satisfying Laplace equations

Explicit formulas for position vectors of such surfaces

Insights into geometric properties in semi-isotropic space

Abstract

A semi-isotropic space is a real affine 3-space endowed with the non-degenerate metric dx^{2}-dy^{2}. The main purpose of this paper is to describe the surfaces of revolution in the semi-isotropic space that satisfy some equations in terms of the position vector and the Laplace operators with respect to the first and the second fundamental forms.