Ruled and quadric surfaces of finite Chen-type

2017/10/19 by Hassan Al-Zoubi, Al-Zoubi, Hassan, Stylianos Stamatakis +3
Mathematics · #53A05 #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1710.07619

openalex publication_date 2017/10/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study ruled surfaces and quadrics in the 3-dimensional Euclidean space which are of finite III-type, that is, they are of finite type, in the sense of B.-Y. Chen, with respect to the third fundamental form. We show that helicoids and spheres are the only ruled and quadric surfaces of finite III-type, respectively.

Related

• Ruled surfaces of finite type with respect to the second fundamental form
• Ruled and quadric surfaces in the 3-dimensional Euclidean space satisfying Δ^III\boldsymbolx = \varLambda \boldsymbolx
• Tubes of finite Chen-type
• Some properties of surfaces of finite III-type
• Surfaces of revolution of finite III-type