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INTEGRATING THE DIFFERENTIAL EQUATIONS INSPIRED BY THE UMBILICITY CONDITION FOR ROTATION HYPERSURFACES IN LORENTZ-MINKOWSKI SPACE

Year 2013, Volume: 6 Issue: 1, 151 - 158, 30.04.2013

Abstract


References

  • [1] Callahan, J. J., Geometry of Spacetime: An Introduction to Special and General Relativity, Springer-Verlag, New York, 2000.
  • [2] Chen, B.-Y., Geometry of submanifolds, M. Dekker, New York, 1973.
  • [3] Chen, B.-Y., An invariant of conformal mappings, Proc. Amer. Math. Soc., 40(1973), pp. 563–564.
  • [4] Chen, B.-Y., Some conformal invariants of submanifolds and their applications, Boll. Un. Mat. Ital., 10(1974), 380–385.
  • [5] Chen, B.-Y., Classification of totally umbilical submanifolds in symmetric spaces, J. Austral. Math. Soc. (Series A), 30(1980), 129–136.
  • [6] Chen, B.-Y., Total mean curvature and submanifolds of finite type, World Scientific, New Jersey, 1984.
  • [7] Chen, B.-Y., Complete classification of spatial surfaces with parallel mean curvature vector in arbitrary non-flat pseudo-Riemannian space forms, Central European J. Math., 7(2009), No.3, pp. 400–428.
  • [8] Chen, B.-Y., Pseudo-Riemannian sumbanifolds, δ-invariants and Applications, World Scien- tific, 2011.
  • [9] Chen, B.-Y. and Garay, O. J. , Complete classification of quasi-minimal surfaces with parallel mean curvature vector in neutral pseudo-Euclidean 4-space E4, Result. Math., 55(2009),23–38.
  • [10] Delaunay, C., Sur la surface de r´evolution dont la courbure moyenne est constante, J. Math. Pure Appl., 6(1841), 309–320.
  • [11] Dursun, U., Rotation hypersurfaces in Lorentz-Minkowski space with constant mean curva- ture, Taiwanese J. of Math., 14(2010), No.2, pp. 685–705.
  • [12] Dursun, U., Turgay, N. C., Minimal and Pseudo-Umbilical Rotational Surfaces in Euclidean Space E4 Mediterr. J. Math. 10 (2013), no. 1, 497–506.
  • [13] Ho, P. T., Remarks on De Sitter Spacetime: Geometry in the Theory of Relativity, Di- mensions, The Journal of Undergraduate Research in Natural Sciences and Mathematics, California State University, Fullerton, 13(2011), pp. 71– 81.
  • [14] Mirsky, L., The spread of a matrix, Mathematika, 3(1956), pp. 127–130.
  • [15] O’Neill, B., Semi-Riemannian geometry with applications to relativity, Academic Press, San Diego, 1983.
  • [16] Spivak, M., A Comprehensive Introduction to Differential Geometry, volume IV, Third edi- tion, Publish or Perish, 1999.
  • [17] Suceav˘a, B. D., The spread of the shape operator as conformal invariant, J. Inequal. Pure Appl. Math. 4 (2003), no. 4, Article 74, 8 pp.
Year 2013, Volume: 6 Issue: 1, 151 - 158, 30.04.2013

Abstract

References

  • [1] Callahan, J. J., Geometry of Spacetime: An Introduction to Special and General Relativity, Springer-Verlag, New York, 2000.
  • [2] Chen, B.-Y., Geometry of submanifolds, M. Dekker, New York, 1973.
  • [3] Chen, B.-Y., An invariant of conformal mappings, Proc. Amer. Math. Soc., 40(1973), pp. 563–564.
  • [4] Chen, B.-Y., Some conformal invariants of submanifolds and their applications, Boll. Un. Mat. Ital., 10(1974), 380–385.
  • [5] Chen, B.-Y., Classification of totally umbilical submanifolds in symmetric spaces, J. Austral. Math. Soc. (Series A), 30(1980), 129–136.
  • [6] Chen, B.-Y., Total mean curvature and submanifolds of finite type, World Scientific, New Jersey, 1984.
  • [7] Chen, B.-Y., Complete classification of spatial surfaces with parallel mean curvature vector in arbitrary non-flat pseudo-Riemannian space forms, Central European J. Math., 7(2009), No.3, pp. 400–428.
  • [8] Chen, B.-Y., Pseudo-Riemannian sumbanifolds, δ-invariants and Applications, World Scien- tific, 2011.
  • [9] Chen, B.-Y. and Garay, O. J. , Complete classification of quasi-minimal surfaces with parallel mean curvature vector in neutral pseudo-Euclidean 4-space E4, Result. Math., 55(2009),23–38.
  • [10] Delaunay, C., Sur la surface de r´evolution dont la courbure moyenne est constante, J. Math. Pure Appl., 6(1841), 309–320.
  • [11] Dursun, U., Rotation hypersurfaces in Lorentz-Minkowski space with constant mean curva- ture, Taiwanese J. of Math., 14(2010), No.2, pp. 685–705.
  • [12] Dursun, U., Turgay, N. C., Minimal and Pseudo-Umbilical Rotational Surfaces in Euclidean Space E4 Mediterr. J. Math. 10 (2013), no. 1, 497–506.
  • [13] Ho, P. T., Remarks on De Sitter Spacetime: Geometry in the Theory of Relativity, Di- mensions, The Journal of Undergraduate Research in Natural Sciences and Mathematics, California State University, Fullerton, 13(2011), pp. 71– 81.
  • [14] Mirsky, L., The spread of a matrix, Mathematika, 3(1956), pp. 127–130.
  • [15] O’Neill, B., Semi-Riemannian geometry with applications to relativity, Academic Press, San Diego, 1983.
  • [16] Spivak, M., A Comprehensive Introduction to Differential Geometry, volume IV, Third edi- tion, Publish or Perish, 1999.
  • [17] Suceav˘a, B. D., The spread of the shape operator as conformal invariant, J. Inequal. Pure Appl. Math. 4 (2003), no. 4, Article 74, 8 pp.
There are 17 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Peter T. Ho This is me

Bogdan D. Sucuevă

Publication Date April 30, 2013
Published in Issue Year 2013 Volume: 6 Issue: 1

Cite

APA Ho, P. T., & Sucuevă, B. D. (2013). INTEGRATING THE DIFFERENTIAL EQUATIONS INSPIRED BY THE UMBILICITY CONDITION FOR ROTATION HYPERSURFACES IN LORENTZ-MINKOWSKI SPACE. International Electronic Journal of Geometry, 6(1), 151-158.
AMA Ho PT, Sucuevă BD. INTEGRATING THE DIFFERENTIAL EQUATIONS INSPIRED BY THE UMBILICITY CONDITION FOR ROTATION HYPERSURFACES IN LORENTZ-MINKOWSKI SPACE. Int. Electron. J. Geom. April 2013;6(1):151-158.
Chicago Ho, Peter T., and Bogdan D. Sucuevă. “INTEGRATING THE DIFFERENTIAL EQUATIONS INSPIRED BY THE UMBILICITY CONDITION FOR ROTATION HYPERSURFACES IN LORENTZ-MINKOWSKI SPACE”. International Electronic Journal of Geometry 6, no. 1 (April 2013): 151-58.
EndNote Ho PT, Sucuevă BD (April 1, 2013) INTEGRATING THE DIFFERENTIAL EQUATIONS INSPIRED BY THE UMBILICITY CONDITION FOR ROTATION HYPERSURFACES IN LORENTZ-MINKOWSKI SPACE. International Electronic Journal of Geometry 6 1 151–158.
IEEE P. T. Ho and B. D. Sucuevă, “INTEGRATING THE DIFFERENTIAL EQUATIONS INSPIRED BY THE UMBILICITY CONDITION FOR ROTATION HYPERSURFACES IN LORENTZ-MINKOWSKI SPACE”, Int. Electron. J. Geom., vol. 6, no. 1, pp. 151–158, 2013.
ISNAD Ho, Peter T. - Sucuevă, Bogdan D. “INTEGRATING THE DIFFERENTIAL EQUATIONS INSPIRED BY THE UMBILICITY CONDITION FOR ROTATION HYPERSURFACES IN LORENTZ-MINKOWSKI SPACE”. International Electronic Journal of Geometry 6/1 (April 2013), 151-158.
JAMA Ho PT, Sucuevă BD. INTEGRATING THE DIFFERENTIAL EQUATIONS INSPIRED BY THE UMBILICITY CONDITION FOR ROTATION HYPERSURFACES IN LORENTZ-MINKOWSKI SPACE. Int. Electron. J. Geom. 2013;6:151–158.
MLA Ho, Peter T. and Bogdan D. Sucuevă. “INTEGRATING THE DIFFERENTIAL EQUATIONS INSPIRED BY THE UMBILICITY CONDITION FOR ROTATION HYPERSURFACES IN LORENTZ-MINKOWSKI SPACE”. International Electronic Journal of Geometry, vol. 6, no. 1, 2013, pp. 151-8.
Vancouver Ho PT, Sucuevă BD. INTEGRATING THE DIFFERENTIAL EQUATIONS INSPIRED BY THE UMBILICITY CONDITION FOR ROTATION HYPERSURFACES IN LORENTZ-MINKOWSKI SPACE. Int. Electron. J. Geom. 2013;6(1):151-8.