Year 2017,
Volume: 5 Issue: 2, 76 - 88, 30.10.2017
Emre Öztürk
,
Yusuf Yaylı
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
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.
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.