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On Elastic Klein Bottle and Fundamental Groups

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Applied Mathematics 2013年第3期4卷 499-504页

作者： A. E. El-Ahmady Taibah University Madinah Saudi Arabia

The purpose of this paper is to give a combinatorial characterization and also construct representations of the fundamental group of the submanifolds of elastic Klein Bottle by using some geometrical transformations. The homotopy groups of the limit elastic Klein Bottle are presented. The fundamental groups of some types of geodesics in elastic Klein Bottle are discussed. New types of homotopy maps are deduced. Theorems governing this connection are achieved.

关键词： Elastic Klein Bottle Homotopy Groups Folding Retraction Deformation retracts

On the Geometry of Curves in Minkowski 3-Space and Its Foldings

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Applied Mathematics 2013年第5期4卷 746-752页

作者： A. E. El-Ahmady E. Al-Hesiny Mathematics Department Faculty of Science Taibah University Madinah KSA

We will introduce a new connection between some transformations and some aspects of differential geometry of some curves in Minkowski space. The concept of folding, retractions and contraction on some curves in Minkowski space will be characterized by using some aspects of differential geometry. Types of the deformation retracts of some curves in Minkowski 3-space are obtained. The relations between the foldings and the deformation retracts of some curves are deduced. The connections between some transformations and time like, space like, light like of some curves in Minkowski 3-space are also presented.

关键词： Retractions Deformation retracts Folding Contraction Minkowski 3-Space

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

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Applied Mathematics 2012年第10期3卷 1153-1160页

作者： Abd El-Aziz El-Ahmady El-Bagoury Asma Salem Al-Luhaybi Mathematics Department Faculty of Science Taibah University Madinah Saudi Arabia Mathematics Department Faculty of Science Tanta University Tanta Egypt

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.

关键词： Retraction Deformation retracts Foldings Flat Robertson-Walker Model

Retractions of One Dimensional Manifold

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Applied Mathematics 2012年第10期3卷 1135-1143页

作者： A. E. El-Ahmady Nashwa Salem Awyd Al-Hazmi Mathematics Department Faculty of Science Taibah University Madinah Saudi Arabia

Our aim in the present article is to introduce and study types of retraction of one dimensional manifold. New types of geodesics in one dimensional manifold are presented. The deformation retracts of one dimensional manifold into itself and onto geodesics is deduced. Also, the isometric and topological folding in each case and the relation between the deformations retracts after and before folding has been obtained. New types of conditional folding are described.

关键词： Retractions Deformation retracts Folding One Dimensional Manifold