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Minimal retraction of space-time and their foldings

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In this article, we will be deduced the geodesics of space-time by using Lagrangian equations. The deformation retract of space-time onto itself and into a geodesics will be achieved. The concept of retraction and folding of zero dimension space-time will be obtained.The relation between limit of folding and retraction presented.

Abstract

In this article, we will be deduced the geodesics of space-time by using Lagrangian equations. The deformation retract of space-time onto itself and into a geodesics will be achieved. The concept of retraction and folding of zero dimension space-time will be obtained.The relation between limit of folding and retraction presented.

참고문헌 (14)

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  2. M. A. Armstrong, "Basic topology" (1979), McGrow-Hill
  3. M. P. Docarmo, "Riemannian geometry" (1992), Birkhauser
  4. A. E. El-Ahmady, "Fuzzy folding of fuzzy horocycle", Tomo, 53, pp.443~450 (2004)
  5. A. E. El-Ahmady, "The deformation retract and topological folding of buchdahi space, periodica", Mathematica Hungarica, 28(1), pp.19~30 (1994)
  6. A. E. El-Ahmady, "Fuzzy Lobachevskian space and its folding", The Joural of Fuzzy Mathematics, 12(2), pp.255~260 (2004)
  7. A. E. El-Ahmady, "Fuzzy deformation retract of fuzzy horospheres", Indian J.pure Appel.Math, 32(10), pp.1501~1506 (2001)
  8. A. E. El-Ahmady, "The deformation retract of a manifold adimting a simple transitive group of motions and its topological folding", Bull. Cal. Math. Soc, 96(4), pp.279~284 (2004)
  9. A. E. El-Ahmady, "Limits of fuzzy retractions of fuzzy hyperspheres and their foldings", Tamkang Journal of Mathematics
  10. A. E. El-Ahmady, "A calculation of geodesics in chaotic flat space and its folding", Chaos, Solitions and Fractals
  11. C. Rogers, "Backland transformations and their applications" (1982), Academic press
  12. M. El-Ghoul, "The folding of minimal manifolds and its deformation", Chaos, Solitons and Fractals U.K., 13, pp.1031~1035 (2002)
  13. M. El-Ghoul, "Folding-retraction of chaotic dynamical manifold and the VAK of vacuum fluction", Chaos, Solitions and Fractal, UK, 20, pp.209~217 (2004)
  14. S. A. Robertson, "Isometric folding of Riemannian manifolds", Proc. Roy. Soc. Edinburgh, 77, pp.275~284 (1977)

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