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A. E. El-Ahmady and H. Rafat, “A Calculation of Geodesics in Chaotic Flat Space and Its Folding,” Chaos, Solutions and Fractals, Vol. 30, 2006, pp. 836-844. Hdoi:10.1016/j.chaos.2005.05.033

has been cited by the following article:

• TITLE: A Geometrical Characterization of Spatially Curved Roberstion-Walker Space and Its Retractions

  AUTHORS: Abd El-Aziz El-Ahmady El-Bagoury, Asma Salem Al-Luhaybi

  KEYWORDS: Retraction; Deformation Retracts; Foldings; Flat Robertson-Walker Model

  JOURNAL NAME: Applied Mathematics, Vol.3 No.10, October 11, 2012

  ABSTRACT: Our aim in the present article is to introduce and study new types of retractions of closed flat Robertson-Walker W4 model. Types of the deformation retract of closed flat Robertson-Walker W4 model are obtained. The relations between the retraction and the deformation retract of curves in W4 model are deduced. Types of minimal retractions of curves in W4 model are also presented. Also, the isometric and topological folding in each case and the relation between the deformation retracts after and before folding have been obtained. New types of homotopy maps are deduced. New types of conditional folding are presented. Some commutative diagrams are obtained.