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arXiv · 0907.3980

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

Ahmad T. Ali·Fathi M. Hamdoon·Rafael Lopez
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Abstract

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.

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Ahmad T. Ali, Fathi M. Hamdoon, Rafael Lopez. 2009-07-23. Constant Scalar Curvature of Three Dimensional Surfaces Obtained by the Equiform Motion of a helix. https://arxiv.org/abs/0907.3980

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