On Surfaces of finite Chen-type

TL;DR

This paper explores the mathematical properties of surfaces in Euclidean space, focusing on their classification as finite type surfaces based on Beltrami operators related to fundamental forms.

Contribution

It introduces new relations involving Beltrami operators for fundamental forms and characterizes finite type surfaces with respect to forms II and III.

Findings

Derived relations between Beltrami operators and fundamental forms.

Characterized finite Chen-type surfaces relative to forms II and III.

Enhanced understanding of surface classifications in differential geometry.

Abstract

We investigate some relations concerning the first and the second Beltrami operators corresponding to the fundamental forms I, II, III of a surface in the three-dimensional Euclidean space and we study surfaces which are of finite type in the sense of B.-Y. Chen with respect to the fundamental forms II and III.