Abstract
In this paper we study three dimensional surfaces in  generated by equiform motions of a pseudohyperbolic surface. The properties of these surfaces up to the first order are investigated. We prove that three dimensional surfaces in  in general, is contained in a canal hypersurface, which is gained as envelope of a one-parametric set of 6-dimensional pseudohyperbolic. Finally we give an example.
Highlights
In this paper we study three dimensional surfaces in E7 generated by equiform motions of a pseudohyperbolic surface
We prove that three dimensional surfaces in E7 in general, is contained in a canal hypersurface, which is gained as envelope of a one-parametric set of
An equiform transformation in the n -dimensional Euclidean space Rn is an affine transformation whose linear part is composed from an orthogonal transformation and a homothetical transformation
Summary
An equiform transformation in the n -dimensional Euclidean space Rn is an affine transformation whose linear part is composed from an orthogonal transformation and a homothetical transformation. In [1, 12], they studied some first order properties of cyclic surfaces generated by the equiform motions in five dimensional Euclidian space and semi-Euclidean space. We restrict our considerations to dimension n = 7 because, at any moment the infinitesimal transformations of the motion maps the points of the pseudohyperbolic surface k to the velocity vectors, whose end points will form an affine image of k (in general a pseudohyperbolic surface k ). Both these surfaces are space and span a subspace W of En with n 7. We show that any three-dimensional surfaces in E7 is in general contained in a canal hypersurface, which is gained as envelope of a one-parametric set of 6-dimensional pseudosphere
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