Kyungpook Mathematical Journal

  • 제46권1호
  • /
  • Pages.139-144
  • /
  • 2006
  • /
  • 1225-6951(pISSN)
  • /
  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
권호 표지

The Invariant of Immersions under Isotwist Folding

  • 투고 : 2004.10.12
  • 발행 : 2006.03.23
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, we will introduce the isotwist foldings of a manifold M into itself. The limits of the isotwist foldings of a manifold are obtained. Also the relations be-tween conditional retraction and this type of the foldings are achieved. Finally the variant and invariant of the immersion under this type of foldings are deduced.

키워드

참고문헌

  1. E. EL-Kholy and M. EL-Ghoul, Simplicial foldings, Journal of the Faculty of Education, 18(1993), 443-455.
  2. E. EL-Kholy and R. M. Shahin, Cellular Folding, Jour. of Inst. of Math Comp. Sci, 3(1998), 177-181.
  3. F. J. C. de Carvalho and S. A. Robertson, Athwart immersion in Euclidean space, Proceedings of the Royal Society of Edinburgh, (to appear).
  4. G. D. Parker, R. S. Millman, Elements of differential geometry, Prentice-Hall New Jersey (1977).
  5. H. R. Farran, E. EL-Kholy and S. A. Robertson, Folding a surface to a polygon, Geometriae Dedicata, 63(1996), 255-266.
  6. M. El-Ghoul, Unfolding of Riemannian manifolds, Commum. Fac. Sci.University of Ankara, A37(1988), 1-4.
  7. M. El-Ghoul, The deformation retract of the complex projective space and its folding, J. of Material Science, 30(1995), England 4145-4148. https://doi.org/10.1007/BF00360722
  8. M. El-Ghoul, Folding of fuzzy torus and fuzzy graphs, Fuzzy Sets and System,Germany (1995).
  9. M. El-Ghoul and M. H. Mostafa, Homology and deformation retract of some real Manifolds and their folding, Bull. Col. Soc, 89(1997), 355-362.
  10. M. El-Ghoul, A. E. Ahmady and H. Rafat, Folding -retracion of chaotic dynamical manifold and VAK of vacuum fluctuation, Chaos, Solitons& Fractals, 20(2004), 209- 217.
  11. M. El-Ghoul, The limit of folding of a manifold and its deformation retract, J. Egyptian Math. Soc., 5(2)(1997), 133-140.
  12. P. Di. Francesco, Folding and coloring problem in mathematics and physics, Bulletien of the American Mathematical Society, 37(3)(2000), 251-307. https://doi.org/10.1090/S0273-0979-00-00870-3
  13. S. A. Robertson, Isometric folding of riemannian manifolds, Proceedings of the Royal Society of Edinburgh, (1977), 275-284.
  14. William S. Massey, Algebraic topology an introduction, Harcourt,Brace World, New York (1967).