Coordinate Finite Type Rotational Surfaces in Euclidean Spaces

Abstract

Abstract. Submanifolds of coordinate finite-type were introduced in [11]. A submanifold of a Euclidean
space is called a coordinate finite-type submanifold if its coordinate functions are eigenfunctions of ∆.
In the present study we consider coordinate finite-type surfaces in E4. We give necessary and sufficient
conditions for generalized rotation surfaces in E4
to become coordinate finite-type. We also give some
special examples.