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Characterizations of dual spacelike curves of constant breadth in dual Lorentzian space D_1^3

Yıl 2016, Cilt: 1 Sayı: 1, 14 - 25, 05.01.2016

Huseyin Kocayigit Muhammet Cetin Beyza Betul Pekacar

Öz

In this paper, we study dual curves of constant breadth in dual Lorentzian Space D13. We obtain the differential equations
characterizing dual curves of constant breadth in  D13 and we introduce some special cases for these dual curves. Furthermore, we obtain
that the total torsion of a closed dual spacelike curve of constant breadth is zero while the total torsion of a simple closed dual timelike
curve is equal to 2nπ, (n ∈ Z). 

Anahtar Kelimeler

Dual Lorentzian space dual Frenet frame dual curve of constant breadth

Kaynakça

  • Ayyıldız, N., C¸ ¨oken, A.C., Y¨ucesan, A., A Characterization of Dual Lorentzian Spherical Curves in the Dual Lorentzian Space, Taiwanese Journal of Mathematics, 11(4), 999-1018, (2007).
  • Ball, N. H., On Ovals, American Mathematical Monthly, 37(7), 348-353, (1930).
  • Barbier, E., Note sur le probleme de l’aiguille et le jeu du joint couvert. J. Math. Pures Appl., II. Ser. 5, 273-286, (1860).
  • Blaschke, W., Konvexe bereiche gegebener konstanter breite und kleinsten inhalts, Mathematische Annalen, B. 76(4), 504-513, (1915).
  • Blaschke, W., Einige Bemerkungen ¨uber Kurven und Fl¨achen konstanter Breite. Ber. Verh. S¨achs. Akad. Leipzig, 67, 290-297,(1915).
  • Blaschke, W., Differential Geometric and Geometrischke Grundlagen ven Einsteins Relativitasttheorie Dover, New York, (1945).
  • Hacısaliho˘glu, H.H., Hareket Geometrisi ve Kuaterniyonlar Teorisi, Gazi Universitesi Fen-Edb. Fak¨ultesi, (1983) ¨
  • Euler, L., De Curvis Triangularibus, Acta Acad. Petropol., 3-30 (1778-1780).
  • Fujivara, M., On space curves of constant breadth, Tohoku Math., J., 5, 180-184, (1914).
  • Kocayi˘git, H., Onder, M., Space curves of constant breadth in Minkowski 3-s ¨ pace, Annali di Matematica, 192(5), 805-814, (2013).
  • Kazaz, M., Onder, M., Kocayigit, H., Spacelike curves of constant breadth in Minkowski 4-space, Int. Journal of Math. Analysis, 22(2), 1061-1068, (2008).
  • Kose, O., On space curves of constant breadth, Do˘ga Tr. J. Math., 1 0(1), 11-14, (1986).
  • Kose, O., Some Properties of Ovals and Curves of Constant Width in a Plane, Doga Mat., 2(8), 119-126, (1984).
  • Magden, A., K¨ose, O., On the curves of constant breadth in E4 space, Turkish J. Math., 21(3), 277-284, (1997).
  • Mellish, A.P., Notes of Differential Geometry, Annals of Mathematics, 32(1), 181-190, (1931).
  • O’Neill, B., Semi-Riemannian Geometry with Applications to Relativity, Academic Press, London, (1983).
  • Onder, M., Kocayigit, H., Candan, E., Differential Equati ¨ ons Characterizing Timelike and Spacelike Curves of Constant Breadth in Minkowski 3-Space E3, 1, J. Korean Math. Soc. 48(4), 849-866, (2011).
  • Sezer, M., Differential equations characterizing space curves of constant breadth and a criterion for these curves, Turkish J. of Math. 13(2), 70-78, (1989).
  • Struik, D. J., Differential Geometry in the Large, Bull. Amer. Math. Soc., 37(2), 49-62, (1931).
  • Ugurlu, H., C¸ alıs¸kan, A., The Study Mapping for Directed Space-like and Time-like Lines in Minkowski 3-Space R3, 1, Math. and Comp. Appl. 1(2), 142-148, (1996).
  • Veldkamp, G.R., On the use of dual numbers, vectors and matrices in instantaneous spatial kinematics, Mech. Mach. Theory, 11(2), 141-156, (1976).
  • Walrave, J., Curves and surfaces in Minkowski space, Doctoral thesis, K. U. Leuven, Fac. of Science, Leuven, (1995).
  • Yılmaz, S., Time-like Dual Curves of Constant Breadth in Dual Lorentzian Space, IBSU Scientific Journal, 2(2), 129-136, (2008).
  • Yılmaz, S., Savcı, U.Z., ¨ Unl¨ut¨urk, Y., On Dual Spacelike Curves of Constant Breadt in Dual Lorentzian Space, New Trends in Mathematical Sciences, 3(4), 164-170, (2015).

Yıl 2016, Cilt: 1 Sayı: 1, 14 - 25, 05.01.2016

Huseyin Kocayigit Muhammet Cetin Beyza Betul Pekacar

Öz

Kaynakça

  • Ayyıldız, N., C¸ ¨oken, A.C., Y¨ucesan, A., A Characterization of Dual Lorentzian Spherical Curves in the Dual Lorentzian Space, Taiwanese Journal of Mathematics, 11(4), 999-1018, (2007).
  • Ball, N. H., On Ovals, American Mathematical Monthly, 37(7), 348-353, (1930).
  • Barbier, E., Note sur le probleme de l’aiguille et le jeu du joint couvert. J. Math. Pures Appl., II. Ser. 5, 273-286, (1860).
  • Blaschke, W., Konvexe bereiche gegebener konstanter breite und kleinsten inhalts, Mathematische Annalen, B. 76(4), 504-513, (1915).
  • Blaschke, W., Einige Bemerkungen ¨uber Kurven und Fl¨achen konstanter Breite. Ber. Verh. S¨achs. Akad. Leipzig, 67, 290-297,(1915).
  • Blaschke, W., Differential Geometric and Geometrischke Grundlagen ven Einsteins Relativitasttheorie Dover, New York, (1945).
  • Hacısaliho˘glu, H.H., Hareket Geometrisi ve Kuaterniyonlar Teorisi, Gazi Universitesi Fen-Edb. Fak¨ultesi, (1983) ¨
  • Euler, L., De Curvis Triangularibus, Acta Acad. Petropol., 3-30 (1778-1780).
  • Fujivara, M., On space curves of constant breadth, Tohoku Math., J., 5, 180-184, (1914).
  • Kocayi˘git, H., Onder, M., Space curves of constant breadth in Minkowski 3-s ¨ pace, Annali di Matematica, 192(5), 805-814, (2013).
  • Kazaz, M., Onder, M., Kocayigit, H., Spacelike curves of constant breadth in Minkowski 4-space, Int. Journal of Math. Analysis, 22(2), 1061-1068, (2008).
  • Kose, O., On space curves of constant breadth, Do˘ga Tr. J. Math., 1 0(1), 11-14, (1986).
  • Kose, O., Some Properties of Ovals and Curves of Constant Width in a Plane, Doga Mat., 2(8), 119-126, (1984).
  • Magden, A., K¨ose, O., On the curves of constant breadth in E4 space, Turkish J. Math., 21(3), 277-284, (1997).
  • Mellish, A.P., Notes of Differential Geometry, Annals of Mathematics, 32(1), 181-190, (1931).
  • O’Neill, B., Semi-Riemannian Geometry with Applications to Relativity, Academic Press, London, (1983).
  • Onder, M., Kocayigit, H., Candan, E., Differential Equati ¨ ons Characterizing Timelike and Spacelike Curves of Constant Breadth in Minkowski 3-Space E3, 1, J. Korean Math. Soc. 48(4), 849-866, (2011).
  • Sezer, M., Differential equations characterizing space curves of constant breadth and a criterion for these curves, Turkish J. of Math. 13(2), 70-78, (1989).
  • Struik, D. J., Differential Geometry in the Large, Bull. Amer. Math. Soc., 37(2), 49-62, (1931).
  • Ugurlu, H., C¸ alıs¸kan, A., The Study Mapping for Directed Space-like and Time-like Lines in Minkowski 3-Space R3, 1, Math. and Comp. Appl. 1(2), 142-148, (1996).
  • Veldkamp, G.R., On the use of dual numbers, vectors and matrices in instantaneous spatial kinematics, Mech. Mach. Theory, 11(2), 141-156, (1976).
  • Walrave, J., Curves and surfaces in Minkowski space, Doctoral thesis, K. U. Leuven, Fac. of Science, Leuven, (1995).
  • Yılmaz, S., Time-like Dual Curves of Constant Breadth in Dual Lorentzian Space, IBSU Scientific Journal, 2(2), 129-136, (2008).
  • Yılmaz, S., Savcı, U.Z., ¨ Unl¨ut¨urk, Y., On Dual Spacelike Curves of Constant Breadt in Dual Lorentzian Space, New Trends in Mathematical Sciences, 3(4), 164-170, (2015).
Toplam 24 adet kaynakça vardır.

Ayrıntılar

Konular Matematik
Bölüm Mathematics, Engineering and statistics
Yazarlar

Huseyin Kocayigit

Muhammet Cetin Bu kişi benim

Beyza Betul Pekacar Bu kişi benim

Yayımlanma Tarihi 5 Ocak 2016
Yayımlandığı Sayı Yıl 2016 Cilt: 1 Sayı: 1

Kaynak Göster

APA Kocayigit, H., Cetin, M., & Pekacar, B. B. (2016). Characterizations of dual spacelike curves of constant breadth in dual Lorentzian space D_1^3. Communication in Mathematical Modeling and Applications, 1(1), 14-25.
AMA Kocayigit H, Cetin M, Pekacar BB. Characterizations of dual spacelike curves of constant breadth in dual Lorentzian space D_1^3. CMMA. Ocak 2016;1(1):14-25.
Chicago Kocayigit, Huseyin, Muhammet Cetin, ve Beyza Betul Pekacar. “Characterizations of Dual Spacelike Curves of Constant Breadth in Dual Lorentzian Space D_1^3”. Communication in Mathematical Modeling and Applications 1, sy. 1 (Ocak 2016): 14-25.
EndNote Kocayigit H, Cetin M, Pekacar BB (01 Ocak 2016) Characterizations of dual spacelike curves of constant breadth in dual Lorentzian space D_1^3. Communication in Mathematical Modeling and Applications 1 1 14–25.
IEEE H. Kocayigit, M. Cetin, ve B. B. Pekacar, “Characterizations of dual spacelike curves of constant breadth in dual Lorentzian space D_1^3”, CMMA, c. 1, sy. 1, ss. 14–25, 2016.
ISNAD Kocayigit, Huseyin vd. “Characterizations of Dual Spacelike Curves of Constant Breadth in Dual Lorentzian Space D_1^3”. Communication in Mathematical Modeling and Applications 1/1 (Ocak 2016), 14-25.
JAMA Kocayigit H, Cetin M, Pekacar BB. Characterizations of dual spacelike curves of constant breadth in dual Lorentzian space D_1^3. CMMA. 2016;1:14–25.
MLA Kocayigit, Huseyin vd. “Characterizations of Dual Spacelike Curves of Constant Breadth in Dual Lorentzian Space D_1^3”. Communication in Mathematical Modeling and Applications, c. 1, sy. 1, 2016, ss. 14-25.
Vancouver Kocayigit H, Cetin M, Pekacar BB. Characterizations of dual spacelike curves of constant breadth in dual Lorentzian space D_1^3. CMMA. 2016;1(1):14-25.