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Some Characterizations of Constant Breadth Spacelike Curves in Minkowski 4-space

Year 2015, Volume: 3 Issue: 2, 1 - 12, 19.01.2015

Hüseyin Kocayiğit Zennure Çiçek

Abstract

In this study, the differential equation characterizations of constant breadth spacelike curves are given in the Minkowski4-space E4. Furthermore, a criterion for a spacelike curve to be a curve of constant breadth in Eis introduced. As an example, theobtained results are applied to the case that the curvatures k, k, k3are constants and are discussed

Keywords

Constant breadth curve spacelike curve; Frenet frame

References

  • Ball, N. H., On ovals, American Mathematical Monthly, 37(7) (1930), 348-353.
  • Barbier, E., Note sur le probl´eme de I’aiguille et le jeu du joint couvert., Journal de Math´ematiques Pures et Appliqu´ees, 2(5) (1860), 273-286.
  • Blaschke, W., Konvexe bereichee gegebener konstanter breite und kleinsten inhalt, Math. Annalen, B. 76 (1915), 504-513.
  • Blaschke, W., Einige Bemerkungen ¨uber Kurven und Fl¨achen konstanter Breite. Ber. Verh. s¨achs. Akad. Leipzig, 67 (1915), 290-2
  • Chung, H.C., A Differential-Geometric Criterion for a Space Curve to be Closed, Proc. Amer. Math. Soc. 83(2) (1981), 357-361.
  • Euler, L., De curvis triangularibus, Acta Acad. Petropol., 3-30, 1778 (1780).
  • Fujivara, M., On space curves of constant breadth, Tohoku Mathematical Journal, 5 (1914), 180-184.
  • Kazaz, M., ¨Onder, M., Kocayiˇgit H., Spacelike curves of constant breadth in Minkowski 4-space, Int. Journal of Math. Analysis, 2(22) (2008), 1061 – 1068.
  • Kocayiˇgit, H., ¨Onder, M., Spacelike curves of constant breadth in Minkowski 3-space, Annali di Matematica, 192(5) (2013), 805-8
  • K¨ose, ¨O., On space curves of constant breadth, Do˘ga Tr. J. Math., 10(1) (1986), 11-14.
  • Maˇgden, A., K¨ose, ¨O., On the curves of constant breadth in E4space, Tr. J. of Mathematics, 21(3) (1997), 277-284.
  • Mellish, A. P., Notes on differential geometry, Annals of Mathematics, 32(1) (1931), 181-190.
  • ¨Onder, M., Kocayiˇgit, H., Candan, E., Differential equations characterizing timelike and spacelike curves of constant breadth in Minkowski 3-space E 3, J. Korean Math. Soc. 48( 1, J. Korean Math. Soc. 48( ), (2011), 849-866.
  • Reuleaux, F., The Kinematics of Machinery, Translated by A.B.W. Kennedy, Dover Pub. Nex York, 1963.
  • Ross, S.L., Differential Equations, John Wiley and Sons, Inc., New York, (1974), 440-468.
  • Sezer, M., Differential equations characterizing space curves of constant breadth and a criterion for these curves, Turkish J. of Math., 13(2) (1989), 70-78.
  • Smakal, S., Curves of constant breadth, Czechoslovak Mathematical Journal, 23() (1973), 86–94.
  • Struik, D.J., Differential Geometry in the Large, Bulletin Amer. Mathem. Soc., 37 (1931), 49-62.
  • Tanaka, H., Kinematics Design of Com Follower Systems, Doctoral Thesis, Columbia Univ., (1976).
  • Walrave, J., Curves and surfaces in Minkowski space, K. U. Leuven, Faculty of Sciences, Ph.D. Thesis, 1995.

Huseyin Kocayi˘git and Zennure C¸ ic¸ek

Year 2015, Volume: 3 Issue: 2, 1 - 12, 19.01.2015

Hüseyin Kocayiğit Zennure Çiçek

Abstract

References

  • Ball, N. H., On ovals, American Mathematical Monthly, 37(7) (1930), 348-353.
  • Barbier, E., Note sur le probl´eme de I’aiguille et le jeu du joint couvert., Journal de Math´ematiques Pures et Appliqu´ees, 2(5) (1860), 273-286.
  • Blaschke, W., Konvexe bereichee gegebener konstanter breite und kleinsten inhalt, Math. Annalen, B. 76 (1915), 504-513.
  • Blaschke, W., Einige Bemerkungen ¨uber Kurven und Fl¨achen konstanter Breite. Ber. Verh. s¨achs. Akad. Leipzig, 67 (1915), 290-2
  • Chung, H.C., A Differential-Geometric Criterion for a Space Curve to be Closed, Proc. Amer. Math. Soc. 83(2) (1981), 357-361.
  • Euler, L., De curvis triangularibus, Acta Acad. Petropol., 3-30, 1778 (1780).
  • Fujivara, M., On space curves of constant breadth, Tohoku Mathematical Journal, 5 (1914), 180-184.
  • Kazaz, M., ¨Onder, M., Kocayiˇgit H., Spacelike curves of constant breadth in Minkowski 4-space, Int. Journal of Math. Analysis, 2(22) (2008), 1061 – 1068.
  • Kocayiˇgit, H., ¨Onder, M., Spacelike curves of constant breadth in Minkowski 3-space, Annali di Matematica, 192(5) (2013), 805-8
  • K¨ose, ¨O., On space curves of constant breadth, Do˘ga Tr. J. Math., 10(1) (1986), 11-14.
  • Maˇgden, A., K¨ose, ¨O., On the curves of constant breadth in E4space, Tr. J. of Mathematics, 21(3) (1997), 277-284.
  • Mellish, A. P., Notes on differential geometry, Annals of Mathematics, 32(1) (1931), 181-190.
  • ¨Onder, M., Kocayiˇgit, H., Candan, E., Differential equations characterizing timelike and spacelike curves of constant breadth in Minkowski 3-space E 3, J. Korean Math. Soc. 48( 1, J. Korean Math. Soc. 48( ), (2011), 849-866.
  • Reuleaux, F., The Kinematics of Machinery, Translated by A.B.W. Kennedy, Dover Pub. Nex York, 1963.
  • Ross, S.L., Differential Equations, John Wiley and Sons, Inc., New York, (1974), 440-468.
  • Sezer, M., Differential equations characterizing space curves of constant breadth and a criterion for these curves, Turkish J. of Math., 13(2) (1989), 70-78.
  • Smakal, S., Curves of constant breadth, Czechoslovak Mathematical Journal, 23() (1973), 86–94.
  • Struik, D.J., Differential Geometry in the Large, Bulletin Amer. Mathem. Soc., 37 (1931), 49-62.
  • Tanaka, H., Kinematics Design of Com Follower Systems, Doctoral Thesis, Columbia Univ., (1976).
  • Walrave, J., Curves and surfaces in Minkowski space, K. U. Leuven, Faculty of Sciences, Ph.D. Thesis, 1995.
There are 20 citations in total.

Details

Journal Section Articles
Authors

Hüseyin Kocayiğit This is me

Zennure Çiçek This is me

Publication Date January 19, 2015
Published in Issue Year 2015 Volume: 3 Issue: 2

Cite

APA Kocayiğit, H., & Çiçek, Z. (2015). Some Characterizations of Constant Breadth Spacelike Curves in Minkowski 4-space. New Trends in Mathematical Sciences, 3(2), 1-12.
AMA Kocayiğit H, Çiçek Z. Some Characterizations of Constant Breadth Spacelike Curves in Minkowski 4-space. New Trends in Mathematical Sciences. January 2015;3(2):1-12.
Chicago Kocayiğit, Hüseyin, and Zennure Çiçek. “Some Characterizations of Constant Breadth Spacelike Curves in Minkowski 4-Space”. New Trends in Mathematical Sciences 3, no. 2 (January 2015): 1-12.
EndNote Kocayiğit H, Çiçek Z (January 1, 2015) Some Characterizations of Constant Breadth Spacelike Curves in Minkowski 4-space. New Trends in Mathematical Sciences 3 2 1–12.
IEEE H. Kocayiğit and Z. Çiçek, “Some Characterizations of Constant Breadth Spacelike Curves in Minkowski 4-space”, New Trends in Mathematical Sciences, vol. 3, no. 2, pp. 1–12, 2015.
ISNAD Kocayiğit, Hüseyin - Çiçek, Zennure. “Some Characterizations of Constant Breadth Spacelike Curves in Minkowski 4-Space”. New Trends in Mathematical Sciences 3/2 (January 2015), 1-12.
JAMA Kocayiğit H, Çiçek Z. Some Characterizations of Constant Breadth Spacelike Curves in Minkowski 4-space. New Trends in Mathematical Sciences. 2015;3:1–12.
MLA Kocayiğit, Hüseyin and Zennure Çiçek. “Some Characterizations of Constant Breadth Spacelike Curves in Minkowski 4-Space”. New Trends in Mathematical Sciences, vol. 3, no. 2, 2015, pp. 1-12.
Vancouver Kocayiğit H, Çiçek Z. Some Characterizations of Constant Breadth Spacelike Curves in Minkowski 4-space. New Trends in Mathematical Sciences. 2015;3(2):1-12.