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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/226305In this paper we consider the equiform motion of a sphere in Euclidean space $\mathbf{E}^7$. We study and analyze the corresponding kinematic three dimensional surface under the hypothesis that its scalar curvature $\mathbf{K}$ is constant. Under this assumption, we prove that $|\mathbf{K}|<2$.11 pages ollyDifferential Geometry53A05; 53A17Constant Scalar Curvature of Three Dimensional Surfaces Obtained by the Equiform Motion of a Spheretext