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

摘要

In this paper we consider the equiform motion of a helix in Euclidean space$\mathbf{E}^7$. We study and analyze the corresponding kinematic threedimensional surface under the hypothesis that its scalar curvature $\mathbf{K}$is constant. Under this assumption, we prove that if the scalar curvature$\mathbf{K}$ is constant, then $\mathbf{K}$ must equal zero.