Three dimensional surfaces foliated by the equiform motion of pseudohyperbolic surfaces in

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.

Calculation Scalar Curvature of the Cycloid Surface in R5

“…An equiform transmutation in the n-dimensional Euclidean space is an affine transmutation whose linear part is composed by an orthogonal transmutation and a homothetical transformation See [2][3][4]. Such an equiform transmutation maps points in according to the rule:…”

Studying Scalar Curvature of Two Dimensional Kinematic Surfaces Obtained by Using Similarity Kinematic of a Deltoid

“…The computation of the first fundamental form of ( ) ( ) 2 2 2 2 2 2 2 1 2 3 1 2 3 1 2 1 3 2 2 1 1 3 3 2 2 2 2 1 2 3 1 1 5 , 2 E. M. Solouma et al 1360 As in the case studied 5  , we have assumed that the original two axis of the deltoid are orthogonal. This means 2 ω ω ω ω ω = = + + .…”

Local Study of Scalar Curvature of Cyclic Surfaces Obtained by Homothetic Motion of Lorentzian Circle

“…be a cyclic surfaces obtained by the homothetic motion of Lorentzian circle c 0 and given by (3) under condition (4that's means the equation(8) hold (i.e., φ be a cyclic surfaces obtained by the homothetic motion of Lorentzian circle c 0 and given by (3) under condition (4). Assume 1 2 0 b b ′ ′ ≠ , then 0 =  on the surface if and only if the following conditions hold:1Cyclic Surfaces with  ≠ 0In this section we assume that the scalar curvature  of the cyclic surface ( ) , X t φ obtained by the homothetic motion of Lorentzian circle 0 c and given by (3) under condition (4) is a non-zero constant.…”