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

Peter T. Ho; Bogdan D. Sucuevă

Araştırma Makalesi

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

Yıl 2013, Cilt: 6 Sayı: 1, 151 - 158, 30.04.2013

Peter T. Ho Bogdan D. Sucuevă

Öz

Anahtar Kelimeler

-

Kaynakça

[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.

Yıl 2013, Cilt: 6 Sayı: 1, 151 - 158, 30.04.2013

Peter T. Ho Bogdan D. Sucuevă

Öz

Kaynakça

[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.

Toplam 17 adet kaynakça vardır.

Ayrıntılar

Birincil Dil	İngilizce
Bölüm	Araştırma Makalesi
Yazarlar	Peter T. Ho Bu kişi benim Bogdan D. Sucuevă
Yayımlanma Tarihi	30 Nisan 2013
Yayımlandığı Sayı	Yıl 2013 Cilt: 6 Sayı: 1

Kaynak Göster

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. Nisan 2013;6(1):151-158.
Chicago	Ho, Peter T., ve 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, sy. 1 (Nisan 2013): 151-58.
EndNote	Ho PT, Sucuevă BD (01 Nisan 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 ve B. D. Sucuevă, “INTEGRATING THE DIFFERENTIAL EQUATIONS INSPIRED BY THE UMBILICITY CONDITION FOR ROTATION HYPERSURFACES IN LORENTZ-MINKOWSKI SPACE”, Int. Electron. J. Geom., c. 6, sy. 1, ss. 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 (Nisan 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. ve Bogdan D. Sucuevă. “INTEGRATING THE DIFFERENTIAL EQUATIONS INSPIRED BY THE UMBILICITY CONDITION FOR ROTATION HYPERSURFACES IN LORENTZ-MINKOWSKI SPACE”. International Electronic Journal of Geometry, c. 6, sy. 1, 2013, ss. 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.