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

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

2009-07-23

arxiv.org/abs/0907.3980v1

Mathematics

Differential Geometry

11 pages, 1 figure

Scientific paper

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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