Algebraic surfaces of the Laplace-Beltrami operators of the TF-type surfaces

TL;DR

This paper investigates algebraic surfaces derived from the Laplace-Beltrami operators of TF-type surfaces in 3D Euclidean space, using computational methods to determine their degrees and classes.

Contribution

It introduces a new class of surfaces called TF-type surfaces and analyzes their Laplace-Beltrami operator surfaces with algebraic and computational techniques.

Findings

Determined degrees and classes of algebraic surfaces of TF-type surfaces.

Applied elimination methods using software to analyze these surfaces.

Provided a framework for studying Laplace-Beltrami operator surfaces of TF-type surfaces.

Abstract

We study on a new kind of surface covered by translation and factorable (TF-type) surfaces in the three dimensional Euclidean space. We consider I and III Laplace-Beltrami operator surfaces of a TF-type surface. Then we obtain degrees and classes of algebraic surfaces of the surfaces using eliminate methods on software programme.