Coordinate Finite Type Rotational Surfaces in Euclidean Spaces

TL;DR

This paper investigates coordinate finite-type surfaces in four-dimensional Euclidean space, providing necessary and sufficient conditions for generalized rotation surfaces to have this property, along with specific examples.

Contribution

It characterizes coordinate finite-type surfaces in E^4 and establishes criteria for generalized rotation surfaces to be of this type.

Findings

Derived necessary and sufficient conditions for generalized rotation surfaces in E^4 to be coordinate finite-type.

Provided explicit examples of such surfaces.

Extended the concept of finite-type submanifolds to higher-dimensional rotational surfaces.

Abstract

Submanifolds of coordinate finite-type were introduced in HV1. A submanifold of a Euclidean space is called a coordinate finite-type submanifold if its coordinate functions are eigenfunctions of {\Delta}. In the present study we consider coordinate finite-type surfaces in E^4. We give necessary and sufficient conditions for generalized rotation surfaces in E^4 to become coordinate finite-type. We also give some special examples.