Constant Scalar Curvature of Three Dimensional Surfaces Obtained by the Equiform Motion of a Sphere

2009/04/09 by Fathi M. Hamdoon, Hamdoon, Fathi M., Ahmad T. Ali +3
Mathematics · Physics and Astronomy · #53A05 #53A17 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Relativity and Gravitational Theory

paper · pdf · doi:10.48550/arxiv.0904.1457

openalex publication_date 2009/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we consider the equiform motion of a sphere in Euclidean space E⁷. We study and analyze the corresponding kinematic three dimensional surface under the hypothesis that its scalar curvature K is constant. Under this assumption, we prove that |K|<2.

Citations

• General helices and a theorem of Lancret

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