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Advances in Mathematical Physics
Volume 2015 (2015), Article ID 301928, 9 pages
Research Article

On the Deformation Retract of Eguchi-Hanson Space and Its Folding

H. Rafat1,2 and Nasr Ahmed1,3

1Mathematics Department, Faculty of Science, Taibah University, Al-Madinah Al-Munawarah 30001, Saudi Arabia
2Department of Mathematics, Faculty of Science, Tanta University, Tanta 31111, Egypt
3Astronomy Department, National Research Institute of Astronomy and Geophysics, Helwan, Cairo 11421, Egypt

Received 20 December 2014; Revised 9 February 2015; Accepted 9 February 2015

Academic Editor: Ivan Avramidi

Copyright © 2015 H. Rafat and Nasr Ahmed. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We introduce the deformation retract of the Eguchi-Hanson space using Lagrangian equations. The retraction of this space into itself and into geodesics has been presented. The deformation retract of the Eguchi-Hanson space into itself and after the isometric folding has been discussed. Theorems concerning these relations have been deduced.