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PARALLEL AND SEMIPARALLEL LIGHTLIKE HYPERSURFACES OF SEMI-RIEMANNIAN SPACE FORMS

Year 2015, Volume: 3 Issue: 1, 95 - 102, 01.04.2015

Abstract

In this paper, some properties of lightlike hypersurfaces with parallel and semiparallel second fundamental forms are investigated in semi-Riemannian space forms. Then some generalizations of these conditions are performed.

References

  • [1] S. Akiba, Submanifolds with zat normal connection and parallel second fundamental tensor, Sci. Repts Yokohama Nat. Univ. Sec. I, 23 (1976), 7-14.
  • [2] J. Deprez, Semi-parallel surfaces in Euclidean space, J. Geom., 25 (1985), 192-200.
  • [3] J. Deprez, Semi-parallel hypersurfaces, Rend. Semin. Mat. Univ. Politec. Torino, 44 (1986), 303-316.
  • [4] F. Dillen, The classi. . . cation of hypersurfaces of a Euclidean space with parallel higher order fundamental form, Math. Z., 203 (1990), 635-643.
  • [5] F. Dillen, Hypersurfaces of a real space form with parallel higher order fundamental form, Soochow J. Math., 18 (1992), 321-338.
  • [6] F. Dillen, Semi-parallel hypersurfaces of a real space form, Israel J. Math., 75 (1991), 193-202.
  • [7] Duggal, K.L. and Bejancu, A., Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, Kluwer Academics Publishers,1996.
  • [8] Duggal, K.L. and Jin, D.H., A classi cation of Einstein lightlike hypersurfaces of a Lorentzian space form, J. Geom. Phys., 60 (2010), 1881-1889.
  • [9] Duggal, K.L. and Sahin, B., Di erential Geometry of Lightlike Submanifolds, Birkhauser Verlag AG, 2010.
  • [10] Gunes, R., Sahin, B. ve Klc, E., On Lightlike Hypersurfaces of a Semi-Riemannian Space Form, Turk. J. Math., 27 (2003), 283-297.
  • [11] U. Lumiste, Semiparallel Submanifolds in Space Forms, Springer, 2009.
  • [12] S. Maeda, Isotropic immersions with parallel second fundamental form, Canad. Math. Bull., 26 (1983), 291-296.
  • [13] M. A. Magid, Isometric immersions of Lorentz space with parallel second fundamental forms, Tsukuba J. Math., 8 (1984), 31-54.
  • [14] V. Mirzoyan, On submanifolds with parallel second fundamental form in spaces of constant curvature, Tartu  Ulik. Toim. Acta Comm. Univ. Tartuensis, 464 (1978), 59-74 (in Russian; summary in English).
  • [15] V. Mirzoyan, On submanifolds with parallel fundamental form of higher order, Dokl. Akad. Nauk Armenian SSR, 66 (1978), 71-75 (in Russian).
  • [16] H. Naitoh, Isotropic submanifolds with parallel second fundamental forms in symmetric spaces, Osaka J. Math., 17 (1980), 95-100.
  • [17] Peterson, P., Riemannian Geometry 2nd Ed., Springer, 2006.
  • [18] Sahin, B., Lightlike Hypersurfaces of Semi-Euclidean Spaces Satisfying Curvature Conditions of Semisymmetry Type, Turk. J. Math., 31 (2007), 139-162.
  • [19] U. Simon and A. Weinstein, Anwendungen der De Rhamschen Zerlegung auf Probleme der lokalen Flachentheorie, Manuscripta Math., 1 (1969), 139-146.
  • [20] M. Takeuchi, Parallel submanifolds of space forms, in Manifolds and Lie Groups: Papers in Honor of Y. Matsushima, Birkhauser, Basel, (1981), 429-447.
  • [21] J. Vilms, Submanifolds of Euclidean space with parallel second fundamental form, Proc. Amer. Math. Soc., 32 (1972), 263-267.
Year 2015, Volume: 3 Issue: 1, 95 - 102, 01.04.2015

Abstract

References

  • [1] S. Akiba, Submanifolds with zat normal connection and parallel second fundamental tensor, Sci. Repts Yokohama Nat. Univ. Sec. I, 23 (1976), 7-14.
  • [2] J. Deprez, Semi-parallel surfaces in Euclidean space, J. Geom., 25 (1985), 192-200.
  • [3] J. Deprez, Semi-parallel hypersurfaces, Rend. Semin. Mat. Univ. Politec. Torino, 44 (1986), 303-316.
  • [4] F. Dillen, The classi. . . cation of hypersurfaces of a Euclidean space with parallel higher order fundamental form, Math. Z., 203 (1990), 635-643.
  • [5] F. Dillen, Hypersurfaces of a real space form with parallel higher order fundamental form, Soochow J. Math., 18 (1992), 321-338.
  • [6] F. Dillen, Semi-parallel hypersurfaces of a real space form, Israel J. Math., 75 (1991), 193-202.
  • [7] Duggal, K.L. and Bejancu, A., Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, Kluwer Academics Publishers,1996.
  • [8] Duggal, K.L. and Jin, D.H., A classi cation of Einstein lightlike hypersurfaces of a Lorentzian space form, J. Geom. Phys., 60 (2010), 1881-1889.
  • [9] Duggal, K.L. and Sahin, B., Di erential Geometry of Lightlike Submanifolds, Birkhauser Verlag AG, 2010.
  • [10] Gunes, R., Sahin, B. ve Klc, E., On Lightlike Hypersurfaces of a Semi-Riemannian Space Form, Turk. J. Math., 27 (2003), 283-297.
  • [11] U. Lumiste, Semiparallel Submanifolds in Space Forms, Springer, 2009.
  • [12] S. Maeda, Isotropic immersions with parallel second fundamental form, Canad. Math. Bull., 26 (1983), 291-296.
  • [13] M. A. Magid, Isometric immersions of Lorentz space with parallel second fundamental forms, Tsukuba J. Math., 8 (1984), 31-54.
  • [14] V. Mirzoyan, On submanifolds with parallel second fundamental form in spaces of constant curvature, Tartu  Ulik. Toim. Acta Comm. Univ. Tartuensis, 464 (1978), 59-74 (in Russian; summary in English).
  • [15] V. Mirzoyan, On submanifolds with parallel fundamental form of higher order, Dokl. Akad. Nauk Armenian SSR, 66 (1978), 71-75 (in Russian).
  • [16] H. Naitoh, Isotropic submanifolds with parallel second fundamental forms in symmetric spaces, Osaka J. Math., 17 (1980), 95-100.
  • [17] Peterson, P., Riemannian Geometry 2nd Ed., Springer, 2006.
  • [18] Sahin, B., Lightlike Hypersurfaces of Semi-Euclidean Spaces Satisfying Curvature Conditions of Semisymmetry Type, Turk. J. Math., 31 (2007), 139-162.
  • [19] U. Simon and A. Weinstein, Anwendungen der De Rhamschen Zerlegung auf Probleme der lokalen Flachentheorie, Manuscripta Math., 1 (1969), 139-146.
  • [20] M. Takeuchi, Parallel submanifolds of space forms, in Manifolds and Lie Groups: Papers in Honor of Y. Matsushima, Birkhauser, Basel, (1981), 429-447.
  • [21] J. Vilms, Submanifolds of Euclidean space with parallel second fundamental form, Proc. Amer. Math. Soc., 32 (1972), 263-267.
There are 21 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Süleyman Cengiz This is me

Publication Date April 1, 2015
Submission Date July 10, 2014
Published in Issue Year 2015 Volume: 3 Issue: 1

Cite

APA Cengiz, S. (2015). PARALLEL AND SEMIPARALLEL LIGHTLIKE HYPERSURFACES OF SEMI-RIEMANNIAN SPACE FORMS. Konuralp Journal of Mathematics, 3(1), 95-102.
AMA Cengiz S. PARALLEL AND SEMIPARALLEL LIGHTLIKE HYPERSURFACES OF SEMI-RIEMANNIAN SPACE FORMS. Konuralp J. Math. April 2015;3(1):95-102.
Chicago Cengiz, Süleyman. “PARALLEL AND SEMIPARALLEL LIGHTLIKE HYPERSURFACES OF SEMI-RIEMANNIAN SPACE FORMS”. Konuralp Journal of Mathematics 3, no. 1 (April 2015): 95-102.
EndNote Cengiz S (April 1, 2015) PARALLEL AND SEMIPARALLEL LIGHTLIKE HYPERSURFACES OF SEMI-RIEMANNIAN SPACE FORMS. Konuralp Journal of Mathematics 3 1 95–102.
IEEE S. Cengiz, “PARALLEL AND SEMIPARALLEL LIGHTLIKE HYPERSURFACES OF SEMI-RIEMANNIAN SPACE FORMS”, Konuralp J. Math., vol. 3, no. 1, pp. 95–102, 2015.
ISNAD Cengiz, Süleyman. “PARALLEL AND SEMIPARALLEL LIGHTLIKE HYPERSURFACES OF SEMI-RIEMANNIAN SPACE FORMS”. Konuralp Journal of Mathematics 3/1 (April 2015), 95-102.
JAMA Cengiz S. PARALLEL AND SEMIPARALLEL LIGHTLIKE HYPERSURFACES OF SEMI-RIEMANNIAN SPACE FORMS. Konuralp J. Math. 2015;3:95–102.
MLA Cengiz, Süleyman. “PARALLEL AND SEMIPARALLEL LIGHTLIKE HYPERSURFACES OF SEMI-RIEMANNIAN SPACE FORMS”. Konuralp Journal of Mathematics, vol. 3, no. 1, 2015, pp. 95-102.
Vancouver Cengiz S. PARALLEL AND SEMIPARALLEL LIGHTLIKE HYPERSURFACES OF SEMI-RIEMANNIAN SPACE FORMS. Konuralp J. Math. 2015;3(1):95-102.
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