Some properties of surfaces of finite III-type

2021/12/31 by Al-Zoubi, Hassan
#53A05 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2201.00659

Abstract

In this paper, we firstly investigate some relations regarding the first and the second Laplace operators corresponding to the third fundamental form III of a surface in the Euclidean space E3. Besides, we introduce the finite Chen type surfaces of revolution with nonvanishing Gauss curvature with respect to the third fundamental form. We present a special case of this family of surfaces of revolution in E3, namely, surfaces of revolution with R is constant, where R denotes the sum of the radii of the principal curvature of a surface.

Related

• Surfaces of revolution of finite III-type
• Surfaces of coordinate finite II-type
• Ruled surfaces of finite type with respect to the second fundamental form
• Ruled and quadric surfaces of finite Chen-type
• Surfaces of coordinate finite type in the Lorentz-Minkowski 3-space