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PARALLEL AND SEMIPARALLEL LIGHTLIKE HYPERSURFACES OF SEMI-RIEMANNIAN SPACE FORMS

Yıl 2015, Cilt: 3 Sayı: 1, 95 - 102, 01.04.2015

Öz

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.

Kaynakça

  • [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.
Yıl 2015, Cilt: 3 Sayı: 1, 95 - 102, 01.04.2015

Öz

Kaynakça

  • [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.
Toplam 21 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Articles
Yazarlar

Süleyman Cengiz Bu kişi benim

Yayımlanma Tarihi 1 Nisan 2015
Gönderilme Tarihi 10 Temmuz 2014
Yayımlandığı Sayı Yıl 2015 Cilt: 3 Sayı: 1

Kaynak Göster

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. Nisan 2015;3(1):95-102.
Chicago Cengiz, Süleyman. “PARALLEL AND SEMIPARALLEL LIGHTLIKE HYPERSURFACES OF SEMI-RIEMANNIAN SPACE FORMS”. Konuralp Journal of Mathematics 3, sy. 1 (Nisan 2015): 95-102.
EndNote Cengiz S (01 Nisan 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., c. 3, sy. 1, ss. 95–102, 2015.
ISNAD Cengiz, Süleyman. “PARALLEL AND SEMIPARALLEL LIGHTLIKE HYPERSURFACES OF SEMI-RIEMANNIAN SPACE FORMS”. Konuralp Journal of Mathematics 3/1 (Nisan 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, c. 3, sy. 1, 2015, ss. 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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