Ruled and quadric surfaces in the 3-dimensional Euclidean space satisfying Δ^III\boldsymbolx = \varLambda \boldsymbolx

2016/10/14 by Hassan Al-Zoubi, Al-Zoubi, Hassan, Stylianos Stamatakis +1
Computer Science · Mathematics · #Algebraic and Geometric Analysis #Computational Geometry and Mesh Generation #Differential Geometry (math.DG) #FOS: Mathematics #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.1610.05102

openalex publication_date 2016/10/14 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28

Abstract

We consider ruled and quadric surfaces in the 3-dimensional Euclidean space which are of coordinate finite type with respect to the third fundamental form III, i.e., their position vector \boldsymbolx satisfies the relation Δ^III\boldsymbolx=\varLambda \boldsymbolx where \varLambda is a square matrix of order 3. We show that helicoids and spheres are the only surfaces in E³ satisfying the preceding relation.

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