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A Geometrical Characterization of Spatially Curved Roberstion-Walker Space and Its Retractions
Mathematics Department, Faculty of Science, Taibah University, Madinah, Saudi Arabia
Mathematics Department, Faculty of Science, Tanta University, Tanta, Egypt
- 1 Mathematics Department, Faculty of Science, Taibah University, Madinah, Saudi Arabia
- 2 Mathematics Department, Faculty of Science, Tanta University, Tanta, Egypt
Applied Mathematics·Volume 03 (2012)·Pages 1153–1160·Published 11 October 2012·DOI10.4236/am.2012.310169
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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.
KeywordsRetractionDeformation RetractsFoldingsFlat Robertson-Walker Model
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