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

Affiliation(s)

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

Mathematics Department, Faculty of Science, Tanta University, Tanta, Egypt.

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

Mathematics Department, Faculty of Science, Tanta University, Tanta, Egypt.

Abstract

Our aim in the present article is to introduce and study new types of retractions of closed flat Robertson-Walker W^{4} model. Types of the deformation retract of closed flat Robertson-Walker W^{4} model are obtained. The relations between the retraction and the deformation retract of curves in W^{4} model are deduced. Types of minimal retractions of curves in W^{4} 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.

Our aim in the present article is to introduce and study new types of retractions of closed flat Robertson-Walker W

Cite this paper

A. El-Bagoury and A. Al-Luhaybi, "A Geometrical Characterization of Spatially Curved Roberstion-Walker Space and Its Retractions,"*Applied Mathematics*, Vol. 3 No. 10, 2012, pp. 1153-1160. doi: 10.4236/am.2012.310169.

A. El-Bagoury and A. Al-Luhaybi, "A Geometrical Characterization of Spatially Curved Roberstion-Walker Space and Its Retractions,"

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