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DIFFERENTIAL GEOMETRY OF CURVES AND SURFACES IN LORENTZ-MINKOWSKI SPACE

Year 2014, , 44 - 107, 30.04.2014

Rafael López

https://doi.org/10.36890/iejg.594497
Cited By: 173

Abstract


Keywords

Lorentz-Minkowski space curve surface curvature Frenet mean curvature

References

  • [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.

Year 2014, , 44 - 107, 30.04.2014

Rafael López

https://doi.org/10.36890/iejg.594497
Cited By: 173

Abstract

References

  • [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.
There are 30 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Rafael López

Publication Date April 30, 2014
Published in Issue Year 2014

Cite

APA López, R. (2014). DIFFERENTIAL GEOMETRY OF CURVES AND SURFACES IN LORENTZ-MINKOWSKI SPACE. International Electronic Journal of Geometry, 7(1), 44-107. https://doi.org/10.36890/iejg.594497
AMA López R. DIFFERENTIAL GEOMETRY OF CURVES AND SURFACES IN LORENTZ-MINKOWSKI SPACE. Int. Electron. J. Geom. April 2014;7(1):44-107. doi:10.36890/iejg.594497
Chicago López, Rafael. “DIFFERENTIAL GEOMETRY OF CURVES AND SURFACES IN LORENTZ-MINKOWSKI SPACE”. International Electronic Journal of Geometry 7, no. 1 (April 2014): 44-107. https://doi.org/10.36890/iejg.594497.
EndNote López R (April 1, 2014) DIFFERENTIAL GEOMETRY OF CURVES AND SURFACES IN LORENTZ-MINKOWSKI SPACE. International Electronic Journal of Geometry 7 1 44–107.
IEEE R. López, “DIFFERENTIAL GEOMETRY OF CURVES AND SURFACES IN LORENTZ-MINKOWSKI SPACE”, Int. Electron. J. Geom., vol. 7, no. 1, pp. 44–107, 2014, doi: 10.36890/iejg.594497.
ISNAD López, Rafael. “DIFFERENTIAL GEOMETRY OF CURVES AND SURFACES IN LORENTZ-MINKOWSKI SPACE”. International Electronic Journal of Geometry 7/1 (April 2014), 44-107. https://doi.org/10.36890/iejg.594497.
JAMA López R. DIFFERENTIAL GEOMETRY OF CURVES AND SURFACES IN LORENTZ-MINKOWSKI SPACE. Int. Electron. J. Geom. 2014;7:44–107.
MLA López, Rafael. “DIFFERENTIAL GEOMETRY OF CURVES AND SURFACES IN LORENTZ-MINKOWSKI SPACE”. International Electronic Journal of Geometry, vol. 7, no. 1, 2014, pp. 44-107, doi:10.36890/iejg.594497.
Vancouver López R. DIFFERENTIAL GEOMETRY OF CURVES AND SURFACES IN LORENTZ-MINKOWSKI SPACE. Int. Electron. J. Geom. 2014;7(1):44-107.

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