Araştırma Makalesi
Yıl 2014,
Cilt: 7 Sayı: 1, 44 - 107, 30.04.2014
Öz
Anahtar Kelimeler
Lorentz-Minkowski space curve surface curvature Frenet mean curvature
Kaynakça
- [1] Abe, N., Koike, N., Yamaguchi, S., Congruence theorems for proper semi-Riemannian hyper- surfaces in a real space form, Yokohama Math. J. 35 (1987), 123–136.
- [2] Barros, M., Caballero, M., Ortega, M., Rotational surfaces in L3 and solitons in the non-linear sigma model, Comm. Math. Phys. 290 (2009), 437–477.
- [3] Bonnor, W. B., Null curves in a Minkowski space-time, Tensor (N. S.) 20 (1969), 229–242.
- [4] Carmo, M. do, Differential Geometry of Curves and Surfaces, Prentice-Hall, Saddle River, 1976.
- [5] Clelland, J. N., Totally quasi-umbilical timelike surfaces in R1,2, Asian J. Math. 16 (2012), no. 2, 189–208.
- [6] Dillen, F., Kühnel, W., Ruled Weingarten surfaces in Minkowski 3-space, Manuscripta Math. 98 (1999), no. 3, 307-320.
- [7] Ferrández, A., Gim´enez, A., Lucas, P., Null helices in Lorentzian space forms, Internat. J. Modern Phys. A 16 (2001), 4845–4863.
- [8] Graves, L. K., Codimension one isometric immersions between Lorentz spaces, Trans. Amer. Math. Soc. 252 (1979), 367–392.
- [9] Hano, J., Nomizu, K., Surfaces of revolution with constant mean curvature in Lorentz- Minkowski space, Tohoku Math. J. 36 (1984), 427–437.
- [10] Inoguchi, J., Lee S., Null curves in Minkowski 3-space, International Elec. J. Geom. 1 (2008), 40–83.
- [11] Klotz, T., Surfaces in Minkowski 3-space on which H and K are linearly related, Michigan Math. J. 30 (1983), 309–315.
- [12] Kobayashi, O., Maximal surfaces in the 3-dimensional Minkowski space L3, Tokyo J. Math. 6 (1983), 297–309.
- [13] Kühnel, W., Differential geometry. Curves – surfaces – manifolds. American Mathematical Society, Providence, RI, 2002.
- [14] Liu, H., Translation surfaces with constant mean curvature in 3-dimensional spaces, J. Geom. 64 (1999), 141–149.
- [15] López, R., Constant mean curvature surfaces with boundary in Euclidean three-space, Tsukuba J. Math. 23 (1999), 27–36.
- [16] López, R., Constant mean curvature hypersurfaces foliated by spheres, Differential Geom. Appl., 11 (1999), 245–256.
- [17] López, R., Cyclic hypersurfaces of constant curvature, Advanced Studies in Pure Mathemat- ics, 34, 2002, Minimal Surfaces, Geometric Analysis and Symplectic Geometry, 185–199.
- [18] López, R., Differential Geometry of Curves and Surfaces in Lorentz-Minkowski Space, ArXiv:0810.3351 (2008).
- [19] López, R., Constant Mean Curvature Surfaces with Boundary, Springer-Verlag, Berlin, 2013.
- [20] López, R., Demir, E., Helicoidal surfaces in Minkowski space with constant mean curvature and constant Gauss curvature, to appear in Central Eur. J. Math.
- [21] Magid, M., Lorentzian isoparametric hypersurface, Pacific. J. Math. 118, (1985), no. 1, 165– 197.
- [22] Mira, P., Pastor, J. A., Helicoidal maximal surfaces in Lorentz-Minkowski space, Monatsh. Math. 140 (2003), 315–334.
- [23] Montiel, S., Ros, A., Curves and Surfaces, Amer. Math. Soc., Graduate Studies in Math. 69. 2009.
- [24] Nesovic, E., Petrovic-Torgasev, M., Verstraelen, L., Curves in Lorentzian spaces, Bolletino U.M.I. 8 (2005), 685–696.
- [25] O’Neill, B., Elementary Differential Geometry, Academic Press, New York, 1966.
- [26] O’Neill, B., Semi-Riemannian Geometry. With applications to relativity. Pure and Applied Mathematics, 103. Academic Press, Inc., New York, 1983.
- [27] B. Riemann, Über die Flächen vom Kleinsten Inhalt be gegebener Begrenzung, Abh. Königl. Ges. Wiss. Gttingen, Math. Kl. 13 (1868), 329–333.
- [28] Walrave, J., Curves and surfaces in Minkowski space, Thesis (Ph.D.), Katholieke Universiteit Leuven (Belgium), 1995.
- [29] Weinstein, T., An Introduction to Lorentz Surfaces, de Gruyter Expositions in Mathematics, 22. Walter de Gruyter & Co., Berlin, 1996.
- [30] Woestijne, I.W., Minimal surfaces in the 3-dimensional Minkowski space. Geometry and Topology of Submanifolds: II, Word Scientic Oress, 344–369, Singapore, 1990.
Yıl 2014,
Cilt: 7 Sayı: 1, 44 - 107, 30.04.2014
Öz
Kaynakça
- [1] Abe, N., Koike, N., Yamaguchi, S., Congruence theorems for proper semi-Riemannian hyper- surfaces in a real space form, Yokohama Math. J. 35 (1987), 123–136.
- [2] Barros, M., Caballero, M., Ortega, M., Rotational surfaces in L3 and solitons in the non-linear sigma model, Comm. Math. Phys. 290 (2009), 437–477.
- [3] Bonnor, W. B., Null curves in a Minkowski space-time, Tensor (N. S.) 20 (1969), 229–242.
- [4] Carmo, M. do, Differential Geometry of Curves and Surfaces, Prentice-Hall, Saddle River, 1976.
- [5] Clelland, J. N., Totally quasi-umbilical timelike surfaces in R1,2, Asian J. Math. 16 (2012), no. 2, 189–208.
- [6] Dillen, F., Kühnel, W., Ruled Weingarten surfaces in Minkowski 3-space, Manuscripta Math. 98 (1999), no. 3, 307-320.
- [7] Ferrández, A., Gim´enez, A., Lucas, P., Null helices in Lorentzian space forms, Internat. J. Modern Phys. A 16 (2001), 4845–4863.
- [8] Graves, L. K., Codimension one isometric immersions between Lorentz spaces, Trans. Amer. Math. Soc. 252 (1979), 367–392.
- [9] Hano, J., Nomizu, K., Surfaces of revolution with constant mean curvature in Lorentz- Minkowski space, Tohoku Math. J. 36 (1984), 427–437.
- [10] Inoguchi, J., Lee S., Null curves in Minkowski 3-space, International Elec. J. Geom. 1 (2008), 40–83.
- [11] Klotz, T., Surfaces in Minkowski 3-space on which H and K are linearly related, Michigan Math. J. 30 (1983), 309–315.
- [12] Kobayashi, O., Maximal surfaces in the 3-dimensional Minkowski space L3, Tokyo J. Math. 6 (1983), 297–309.
- [13] Kühnel, W., Differential geometry. Curves – surfaces – manifolds. American Mathematical Society, Providence, RI, 2002.
- [14] Liu, H., Translation surfaces with constant mean curvature in 3-dimensional spaces, J. Geom. 64 (1999), 141–149.
- [15] López, R., Constant mean curvature surfaces with boundary in Euclidean three-space, Tsukuba J. Math. 23 (1999), 27–36.
- [16] López, R., Constant mean curvature hypersurfaces foliated by spheres, Differential Geom. Appl., 11 (1999), 245–256.
- [17] López, R., Cyclic hypersurfaces of constant curvature, Advanced Studies in Pure Mathemat- ics, 34, 2002, Minimal Surfaces, Geometric Analysis and Symplectic Geometry, 185–199.
- [18] López, R., Differential Geometry of Curves and Surfaces in Lorentz-Minkowski Space, ArXiv:0810.3351 (2008).
- [19] López, R., Constant Mean Curvature Surfaces with Boundary, Springer-Verlag, Berlin, 2013.
- [20] López, R., Demir, E., Helicoidal surfaces in Minkowski space with constant mean curvature and constant Gauss curvature, to appear in Central Eur. J. Math.
- [21] Magid, M., Lorentzian isoparametric hypersurface, Pacific. J. Math. 118, (1985), no. 1, 165– 197.
- [22] Mira, P., Pastor, J. A., Helicoidal maximal surfaces in Lorentz-Minkowski space, Monatsh. Math. 140 (2003), 315–334.
- [23] Montiel, S., Ros, A., Curves and Surfaces, Amer. Math. Soc., Graduate Studies in Math. 69. 2009.
- [24] Nesovic, E., Petrovic-Torgasev, M., Verstraelen, L., Curves in Lorentzian spaces, Bolletino U.M.I. 8 (2005), 685–696.
- [25] O’Neill, B., Elementary Differential Geometry, Academic Press, New York, 1966.
- [26] O’Neill, B., Semi-Riemannian Geometry. With applications to relativity. Pure and Applied Mathematics, 103. Academic Press, Inc., New York, 1983.
- [27] B. Riemann, Über die Flächen vom Kleinsten Inhalt be gegebener Begrenzung, Abh. Königl. Ges. Wiss. Gttingen, Math. Kl. 13 (1868), 329–333.
- [28] Walrave, J., Curves and surfaces in Minkowski space, Thesis (Ph.D.), Katholieke Universiteit Leuven (Belgium), 1995.
- [29] Weinstein, T., An Introduction to Lorentz Surfaces, de Gruyter Expositions in Mathematics, 22. Walter de Gruyter & Co., Berlin, 1996.
- [30] Woestijne, I.W., Minimal surfaces in the 3-dimensional Minkowski space. Geometry and Topology of Submanifolds: II, Word Scientic Oress, 344–369, Singapore, 1990.
Toplam 30 adet kaynakça vardır.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Bölüm | Araştırma Makalesi |
| Yazarlar | |
| Yayımlanma Tarihi | 30 Nisan 2014 |
| Yayımlandığı Sayı | Yıl 2014 Cilt: 7 Sayı: 1 |