Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2017, Cilt: 5 Sayı: 2, 76 - 88, 30.10.2017
https://doi.org/10.36753/mathenot.421740

Öz

Kaynakça

  • [1] Rademacher, H. and Toeplitz, O., The enjoyment of mathematics. Princeton Science Library Princeton University Press, 1994.
  • [2] Kerzman, N. and Stein, E. M., The Cauchy Kernel, the Szegö Kernel, and the Riemann Mapping Function. Math.Ann. 236 (1978),85-93.
  • [3] Boas, H. P., A Geometric Characterization of the Ball and the Bochner-Martinelli Kernel. Math. Ann. 248 (1980), 275-278.
  • [4] Boas, H. P., Spheres and Cylinders: A Local Geometric Characterization. Illinois Journal of Mathematics. 28 (1984), Spring, no. 1, 120-124.
  • [5] Wegner, B., A Differential Geometric Proof of the Local Geometric Characterization of Spheres and Cylinders by Boas. Mathematica Balkanica. 2 (1988), 294-295.
  • [6] Chen, B.Y., Kim D.S. and Kim Y.H., New Characterizations of W-Curves. Publ. Math. Debrecen. 69 (2006), no. 4, 457-472.
  • [7] Kim, D.S. and Kim Y.H., New Characterizations of Spheres, Cylinders and W-Curves. Linear Algebra and Its Applications. 432 (2010), 3002-3006.
  • [8] Kim, H.Y. and Lee, K.E., Surfaces of Euclidean 4-Space Whose Geodesics are W-Curves. Nihonkai Math. J. 4 (1993), 221-232.
  • [9] Öztürk, G., Arslan, K. and Hacısalihoğlu, H. H., A Characterization of CCR-Curves in R^m. Proceedings of the Estonian Academy of Sciences. 57 (2008), no. 4, 217-224.
  • [10] Aminov, Y., Differential Geometry and Topology of Curves. Gordon and Breach Science Publishers imprint London, 2000.
  • [11] Torgašev, M. P. and Šucurovic, E., W−Curves in Minkowski Space-Time. Novi Sad J. Math. 32 (2002), no. 2, 55-65.
  • [12]İyigün, E. and Arslan, K., On Harmonic Curvatures Of Curves In Lorentzian n−Space Commun. Fac. Sci. Univ. Ank. Series A1. 54 (2005), no. 1, 29-34.
  • [13] İlarslan, K. and Boyacıo ˘glu, Ö., Position Vectors of a Spacelike W−curve in Minkowski Space R_^3. Bull. Korean Math. Soc. 44 (2007), no. 3, 429-438.
  • [14] Önder, M. and Uğurlu, H.H., Frenet Frames and Invariants of Timelike Ruled Surfaces. Ain Shams Engineering Journal. 4 (2013), 507-513.
  • [15] Walrave, J., Curves and Surfaces in Minkowski Space. Doctoral Dissertation K. U. Leuven, Fac.of Science, Leuven, 1995.
  • [16] Kühnel, W., Differential Geometry Curves-Surfaces-Manifolds. American Mathematical Society, 2006.
  • [17] O’Neill, B., Semi-Riemann Geometry with Applications to Relativity, Academic Press. Inc., 1983.
  • [18] Acratalishian, A., On Linear Vector Fields in R^2n+1 Euclidean Space. Gazi University, Institute of Science and Technology, Doctoral Dissertation, Ankara, 1989.
  • [19] Karger, A. and Novak, J., Space Kinematics and Lie Groups. Gordon and Breach Science Publishers, 1985.
  • [20] Ünal, Z., Kinematics with Algebraic Methods In Lorentzian Spaces. Ankara University, Doctoral Dissertation, Ankara, 2007.
  • [21] Lopez, R., Differential Geometry of Curves and Surfaces in Lorentz-Minkowski space. Int.Electron. J. Geom. 7 (2014), 44-107.
  • [22] Munteanu, M.I. and Nistor A.I., The classification of Killing magnetic curves in S^2 × R Journal of Geometry and Physics. 62 (2012), 170-182.

W-Curves in Lorentz-Minkowski Space

Yıl 2017, Cilt: 5 Sayı: 2, 76 - 88, 30.10.2017
https://doi.org/10.36753/mathenot.421740

Öz

In this paper, we investigate the chord properties of the non-null W-curves in Lorentz-Minkowski space.
We give the general equation form for W-curves in (2n+1)-dimension. We define some special curves and
give the relations between these curves and isoparametric surfaces. Finally we obtain the geodesics of the
pseudospherical cylinder and pseudohyperbolic cylinder in 4-dimensional space.

Kaynakça

  • [1] Rademacher, H. and Toeplitz, O., The enjoyment of mathematics. Princeton Science Library Princeton University Press, 1994.
  • [2] Kerzman, N. and Stein, E. M., The Cauchy Kernel, the Szegö Kernel, and the Riemann Mapping Function. Math.Ann. 236 (1978),85-93.
  • [3] Boas, H. P., A Geometric Characterization of the Ball and the Bochner-Martinelli Kernel. Math. Ann. 248 (1980), 275-278.
  • [4] Boas, H. P., Spheres and Cylinders: A Local Geometric Characterization. Illinois Journal of Mathematics. 28 (1984), Spring, no. 1, 120-124.
  • [5] Wegner, B., A Differential Geometric Proof of the Local Geometric Characterization of Spheres and Cylinders by Boas. Mathematica Balkanica. 2 (1988), 294-295.
  • [6] Chen, B.Y., Kim D.S. and Kim Y.H., New Characterizations of W-Curves. Publ. Math. Debrecen. 69 (2006), no. 4, 457-472.
  • [7] Kim, D.S. and Kim Y.H., New Characterizations of Spheres, Cylinders and W-Curves. Linear Algebra and Its Applications. 432 (2010), 3002-3006.
  • [8] Kim, H.Y. and Lee, K.E., Surfaces of Euclidean 4-Space Whose Geodesics are W-Curves. Nihonkai Math. J. 4 (1993), 221-232.
  • [9] Öztürk, G., Arslan, K. and Hacısalihoğlu, H. H., A Characterization of CCR-Curves in R^m. Proceedings of the Estonian Academy of Sciences. 57 (2008), no. 4, 217-224.
  • [10] Aminov, Y., Differential Geometry and Topology of Curves. Gordon and Breach Science Publishers imprint London, 2000.
  • [11] Torgašev, M. P. and Šucurovic, E., W−Curves in Minkowski Space-Time. Novi Sad J. Math. 32 (2002), no. 2, 55-65.
  • [12]İyigün, E. and Arslan, K., On Harmonic Curvatures Of Curves In Lorentzian n−Space Commun. Fac. Sci. Univ. Ank. Series A1. 54 (2005), no. 1, 29-34.
  • [13] İlarslan, K. and Boyacıo ˘glu, Ö., Position Vectors of a Spacelike W−curve in Minkowski Space R_^3. Bull. Korean Math. Soc. 44 (2007), no. 3, 429-438.
  • [14] Önder, M. and Uğurlu, H.H., Frenet Frames and Invariants of Timelike Ruled Surfaces. Ain Shams Engineering Journal. 4 (2013), 507-513.
  • [15] Walrave, J., Curves and Surfaces in Minkowski Space. Doctoral Dissertation K. U. Leuven, Fac.of Science, Leuven, 1995.
  • [16] Kühnel, W., Differential Geometry Curves-Surfaces-Manifolds. American Mathematical Society, 2006.
  • [17] O’Neill, B., Semi-Riemann Geometry with Applications to Relativity, Academic Press. Inc., 1983.
  • [18] Acratalishian, A., On Linear Vector Fields in R^2n+1 Euclidean Space. Gazi University, Institute of Science and Technology, Doctoral Dissertation, Ankara, 1989.
  • [19] Karger, A. and Novak, J., Space Kinematics and Lie Groups. Gordon and Breach Science Publishers, 1985.
  • [20] Ünal, Z., Kinematics with Algebraic Methods In Lorentzian Spaces. Ankara University, Doctoral Dissertation, Ankara, 2007.
  • [21] Lopez, R., Differential Geometry of Curves and Surfaces in Lorentz-Minkowski space. Int.Electron. J. Geom. 7 (2014), 44-107.
  • [22] Munteanu, M.I. and Nistor A.I., The classification of Killing magnetic curves in S^2 × R Journal of Geometry and Physics. 62 (2012), 170-182.
Toplam 22 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Articles
Yazarlar

Emre Öztürk

Yusuf Yaylı

Yayımlanma Tarihi 30 Ekim 2017
Gönderilme Tarihi 6 Ekim 2017
Yayımlandığı Sayı Yıl 2017 Cilt: 5 Sayı: 2

Kaynak Göster

APA Öztürk, E., & Yaylı, Y. (2017). W-Curves in Lorentz-Minkowski Space. Mathematical Sciences and Applications E-Notes, 5(2), 76-88. https://doi.org/10.36753/mathenot.421740
AMA Öztürk E, Yaylı Y. W-Curves in Lorentz-Minkowski Space. Math. Sci. Appl. E-Notes. Ekim 2017;5(2):76-88. doi:10.36753/mathenot.421740
Chicago Öztürk, Emre, ve Yusuf Yaylı. “W-Curves in Lorentz-Minkowski Space”. Mathematical Sciences and Applications E-Notes 5, sy. 2 (Ekim 2017): 76-88. https://doi.org/10.36753/mathenot.421740.
EndNote Öztürk E, Yaylı Y (01 Ekim 2017) W-Curves in Lorentz-Minkowski Space. Mathematical Sciences and Applications E-Notes 5 2 76–88.
IEEE E. Öztürk ve Y. Yaylı, “W-Curves in Lorentz-Minkowski Space”, Math. Sci. Appl. E-Notes, c. 5, sy. 2, ss. 76–88, 2017, doi: 10.36753/mathenot.421740.
ISNAD Öztürk, Emre - Yaylı, Yusuf. “W-Curves in Lorentz-Minkowski Space”. Mathematical Sciences and Applications E-Notes 5/2 (Ekim 2017), 76-88. https://doi.org/10.36753/mathenot.421740.
JAMA Öztürk E, Yaylı Y. W-Curves in Lorentz-Minkowski Space. Math. Sci. Appl. E-Notes. 2017;5:76–88.
MLA Öztürk, Emre ve Yusuf Yaylı. “W-Curves in Lorentz-Minkowski Space”. Mathematical Sciences and Applications E-Notes, c. 5, sy. 2, 2017, ss. 76-88, doi:10.36753/mathenot.421740.
Vancouver Öztürk E, Yaylı Y. W-Curves in Lorentz-Minkowski Space. Math. Sci. Appl. E-Notes. 2017;5(2):76-88.

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