Retractions of One Dimensional Manifold

Affiliation(s)

Mathematics Department, Faculty of Science, Taibah University, Madinah, Saudi Arabia.

Mathematics Department, Faculty of Science, Taibah University, Madinah, Saudi Arabia.

Abstract

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.

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.

Cite this paper

A. El-Ahmady and N. Al-Hazmi, "Retractions of One Dimensional Manifold,"*Applied Mathematics*, Vol. 3 No. 10, 2012, pp. 1135-1143. doi: 10.4236/am.2012.310167.

A. El-Ahmady and N. Al-Hazmi, "Retractions of One Dimensional Manifold,"

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