arXiv subjects

Fathi M. Hamdoon

Publications and source records attributed to Fathi M. Hamdoon.

2 recordsLinked to original sources

arXiv2009

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

In this paper we consider the equiform motion of a helix 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 if the scalar curvature $\mathbf{K}$ is constant, then $\mathbf{K}$ must equal zero.

math.DG↗

arXiv2009

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

In 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 $|\mathbf{K}|<2$.

math.DG↗