Helicoidal surfaces of finite type in the 3-dimensional Heisenberg group

Abstract

An Euclidean submanifold is said to be of finite Chen-type if its coordinate functions are a finite sum of eigenfunctions of its Laplacian [6]. In this article, we study helicoidal invariant surfaces in the 3-dimensional Heisenberg group H₃, which has finite type immersion.

Subject Classification: (2010):

• 53C30
• 53B25

Keywords:

• Laplacian operator
• Heisenberg group
• Invariant surface
• Surfaces of coordinate finite type