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

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

2009-04-09

arxiv.org/abs/0904.1457v1

Mathematics

Differential Geometry

11 pages olly

Scientific paper

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

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