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DIFFERENTIAL EQUATIONS CHARACTERIZING TIMELIKE AND SPACELIKE CURVES OF CONSTANT BREADTH IN MINKOWSKI 3-SPACE <수식>

Huseyin Kocayigit|Mehmet Onder|Elif Candan
대한수학회 (The Korean Mathematical Society)|2011.07|대한수학회지 (Journal of the KMS)|제48권 제4호|pp. 849-866

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참고문헌

키워드

Minkowski 3-spacetimelike curvespacelike curveconstant breadth curve
주제분류수학

초록

In this paper, we give the differential equations characterizing the timelike and spacelike curves of constant breadth in Minkowski 3-space <수식>. Furthermore, we give a criterion for a timelike or spacelike curve to be the curve of constant breadth in <수식>. As an example, the obtained results are applied to the case ρ = const: and k_2 = const:, and are discussed.

Abstract

In this paper, we give the differential equations characterizing the timelike and spacelike curves of constant breadth in Minkowski 3-space <수식>. Furthermore, we give a criterion for a timelike or spacelike curve to be the curve of constant breadth in <수식>. As an example, the obtained results are applied to the case ρ = const: and k_2 = const:, and are discussed.

참고문헌 (20)

  1. N. H. Ball, "On Ovals", Amer. Math. Monthly, 37(7), pp.348~353 (1930)
  2. E. Barbier, "J. de Math", 2(5), pp.272~286 (1860)
  3. W. Blaschke, "Konvexe Bereiche gegebener konstanter Breite und kleinsten Inhalts", Math. Ann, 76(4), pp.504~513 (1915)
  4. W. Blaschke, "Leibziger Berichte", 67, pp.290~ (1917)
  5. S. Breuer, "The Reduction of Linear Ordinary Differential Equations to Equations with Constant Coefficients", J. Math. Anal. Appl, 32(1), pp.62~76 (1970)
  6. H. C. Chung, "differential-geometric criterion for a space curve to be closed", Proc. Amer. Math. Soc, 83(2), pp.357~361 (1981)
  7. L. Euler, "De curvis triangularibus", Acta Acad. Prtropol, pp.3~30
  8. M. Fujivara, "On space curves of constant breadth", Tohoku Math. J, 5, pp.179~784 (1914)
  9. M. Kazaz, "Spacelike curves of constant breadth in Minkowski 4-space", Int. J. Math. Anal, 2(21), pp.1061~1068 (2008)
  10. O. Kose, "On space curves of constant breadth", Doga Mat, 10(1), pp.11~14 (1986)
  11. A. Maden, "On the curves of constant breadth in E4 space", Turkish J. Math, 21(3), pp.277~284 (1997)
  12. A. P. Mellish, "Notes on differential geometry", Ann. of Math, 32(1), pp.181~190 (1931)
  13. B. O'Neil, "Semi-Riemannian Geometry with Applications to Relativity" (1983), Academic Press
  14. F. Reuleaux, "The Kinematics of Machinery" (1963), Dover, Pub
  15. S. L. Ross, "Differential Equations" (1974), John Wiley and Sons, Inc
  16. M. Sezer, "Differential equations characterizing space curves of constant breadth and a criterion for these curves", Doga Mat, 13(2), pp.70~78 (1989)
  17. S. Smakal, "Curves of constant breadth", Czechoslovak Math. J, 23, pp.86~94 (1973)
  18. D. J. Struik, "Differential geometry in the large", Bull. Amer. Math. Soc, 37(2), pp.49~62 (1931)
  19. H. Tanaka, "Kinematics Design of Com Follower Systems", 박사, pp.1976
  20. J. Walrave, "Curves and Surfaces in Minkowski Space", 박사, pp.1995

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