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DIFFERENTIAL GEOMETRY OF CURVES AND SURFACES IN LORENTZ-MINKOWSKI SPACE

Year 2014, Volume: 7 Issue: 1 , 44 - 107 , 30.04.2014
https://doi.org/10.36890/iejg.594497
https://izlik.org/JA25AN93AB

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.

Year 2014, Volume: 7 Issue: 1 , 44 - 107 , 30.04.2014
https://doi.org/10.36890/iejg.594497
https://izlik.org/JA25AN93AB

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
DOI https://doi.org/10.36890/iejg.594497
IZ https://izlik.org/JA25AN93AB
Published in Issue Year 2014 Volume: 7 Issue: 1

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 1.López R. DIFFERENTIAL GEOMETRY OF CURVES AND SURFACES IN LORENTZ-MINKOWSKI SPACE. Int. Electron. J. Geom. 2014;7(1):44-107. doi:10.36890/iejg.594497
Chicago López, Rafael. 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.
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 [1]R. López, “DIFFERENTIAL GEOMETRY OF CURVES AND SURFACES IN LORENTZ-MINKOWSKI SPACE”, Int. Electron. J. Geom., vol. 7, no. 1, pp. 44–107, Apr. 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 1, 2014): 44-107. https://doi.org/10.36890/iejg.594497.
JAMA 1.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, Apr. 2014, pp. 44-107, doi:10.36890/iejg.594497.
Vancouver 1.Rafael López. DIFFERENTIAL GEOMETRY OF CURVES AND SURFACES IN LORENTZ-MINKOWSKI SPACE. Int. Electron. J. Geom. 2014 Apr. 1;7(1):44-107. doi:10.36890/iejg.594497

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