Research Article
BibTex RIS Cite

Year 2017, Volume: 5 Issue: 2, 76 - 88, 30.10.2017

Emre Öztürk Yusuf Yaylı

https://doi.org/10.36753/mathenot.421740
Cited By: 5

Abstract

References

  • [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

Year 2017, Volume: 5 Issue: 2, 76 - 88, 30.10.2017

Emre Öztürk Yusuf Yaylı

https://doi.org/10.36753/mathenot.421740
Cited By: 5

Abstract

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.

Keywords

W-curve isoparametric surface Lorentz-Minkowski space

References

  • [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.
There are 22 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Emre Öztürk

Yusuf Yaylı

Publication Date October 30, 2017
Submission Date October 6, 2017
Published in Issue Year 2017 Volume: 5 Issue: 2

Cite

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. October 2017;5(2):76-88. doi:10.36753/mathenot.421740
Chicago Öztürk, Emre, and Yusuf Yaylı. “W-Curves in Lorentz-Minkowski Space”. Mathematical Sciences and Applications E-Notes 5, no. 2 (October 2017): 76-88. https://doi.org/10.36753/mathenot.421740.
EndNote Öztürk E, Yaylı Y (October 1, 2017) W-Curves in Lorentz-Minkowski Space. Mathematical Sciences and Applications E-Notes 5 2 76–88.
IEEE E. Öztürk and Y. Yaylı, “W-Curves in Lorentz-Minkowski Space”, Math. Sci. Appl. E-Notes, vol. 5, no. 2, pp. 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 (October 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 and Yusuf Yaylı. “W-Curves in Lorentz-Minkowski Space”. Mathematical Sciences and Applications E-Notes, vol. 5, no. 2, 2017, pp. 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.

Cited By

A nonlinear transformation between space curves defined by curvature-torsion relations in 3-dimensional Euclidean space
Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics
https://doi.org/10.31801/cfsuasmas.1083750
Elementary Approachs on De Sitter Space
Mathematical Sciences and Applications E-Notes
https://doi.org/10.36753/mathenot.583477
Gauss Map and Local Approach of Isoparametric Surfaces in Lorentz and Euclidean Space
Fundamental Journal of Mathematics and Applications
https://doi.org/10.33401/fujma.643374
Application of Matrix Methods On W-Curves
International Electronic Journal of Geometry
https://doi.org/10.36890/iejg.690484
A Dynamical Approach to Position Vector of Timelike Curve by Vectorial Momentum, Torque and Tangential Dual Curve
Journal of Nonlinear Mathematical Physics
https://doi.org/10.1007/s44198-022-00061-w

20477

The published articles in MSAEN are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.