Araştırma Makalesi
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Bir Belirsiz Para Sasakiyan Manifoldun Lightlike Hiperyüzeyleri

Yıl 2019, Cilt: 9 Sayı: 2, 352 - 373, 30.12.2019
https://doi.org/10.37094/adyujsci.516251

Öz

Bu makalede, bir belirsiz para Sasakiyan manifoldun yapı vektör alanına teğet olan lightlike hiperyüzeyleri çalışılmıştır. Özel olarak, değişmez lightlike hiperyüzeyler ve ekran yarı-değişmez lightlike hiperyüzeyler tanıtılarak bazı örnekler verilmiştir. Bir belirsiz para Sasakian manifoldun ekran yarı-değişmez lightlike hiperyüzeyine dahil olan distribüsyonlar için integrallenebilirlik koşulları incelenmiştir.

Kaynakça

  • [1] Küpeli, D.N., On null submanifolds in spacetimes, Geometriae Dedicata, 23(1), 33-51, 1987.
  • [2] Bejancu, A., Duggal, K.L., Real hypersurfaces of indefinite Kaehler manifolds, International Journal of Mathematics and Mathematical Sciences, 16(3), 545-556, 1993.
  • [3] Duggal, K.L., Şahin, B., Differential geometry of lightlike submanifolds, Frontiers in Mathematics. Birkhäuser Verlag, Basel, 2010.
  • [4] Sasaki, S., On differentiable manifolds with certain structures which are closely related to almost contact structure , Tohoku Mathematical Journal, (2) 12, 459-476, 1960.
  • [5] Blair, D.E., Riemannian geometry of contact and symplectic manifolds (Second edition) Progress in Mathematics, 203. Birkhauser Boston, Inc., Boston, MA, 2010.
  • [6] Sato, I., On a structure similar to the almost contact structure, Tensor (N.S.), 30(3), 219-224, 1976.
  • [7] Takahashi, T., Sasakian manifold with pseudo-Riemannian metric, Tohoku Mathematical Journal, 21(2), 271-290, 1969.
  • [8] Duggal, K.L., Bejancu, A., Lightlike submanifolds of semi-Riemannian manifolds and its applications, Mathematics and its Applications, 364. Kluwer Academic Publishers Group, Dordrecht, 1996.
  • [9] Duggal, K.L., Space time manifolds and contact structures, International Journal of Mathematics and Mathematical Sciences, 13(3), 545-553, 1990.
  • [10] Duggal, K.L., Şahin, B., Lightlike submanifolds of indefinite Sasakian manifolds, International Journal of Mathematics and Mathematical Sciences, Art. ID 57585, 21 pp., 2007.
  • [11] Kang, T.H., Jung, S.D., Kim, B.H., Pak, H.K., Pak, J.S., Lightlike hypersurfaces of indefinite Sasakian manifolds, Indian Journal of Pure and Applied Mathematics, 34 (9), 1369-1380, 2003.
  • [12] Matsumoto, K., On Lorentzian paracontact manifolds, Bullet in of the Yamagata University, Natural Science, 12(2), 151-156, 1989.
  • [13] Tripathi, M.M., Kılıç, E., Yüksel Perktaş, S., Keleş, S., Indefinite almost paracontact metric manifolds, International Journal of Mathematics and Mathematical Sciences, Art. Id. 846195, pp. 19, 2010.
  • [14] Yüksel Perktaş, S., Kılıç, E., Tripathi, M.M., Keleş, S., On indefinite - para Sasakian -manifolds, International Journal of Pure and Applied Mathematics, 77(4), 485-499, 2012.
  • [15] Shukla, S.S., Yadev, A., Radical transversal lightlike submanifolds of indefinite para-Sasakian manifolds, Demonstratio Mathematica, vol. XVLVII, No. 4, 994-1011, 2014.
  • [16] Shukla, S.S., Yadev, A., Lightlike submanifolds of indefinite para-Sasakian manifolds, Matematicki Vesnik, 66 (4), 371-386, 2014.
  • [17] O’Neill, B., Semi-Riemannian geometry with applications to relativity, Pure and Applied Mathematics, 103. Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York, 1983.
  • [18] Duggal, K.L., Jin, D.H., Null Curves and Hypersurfaces of Semi-Riemannian Manifolds, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2007.
  • [19] Beem, J.K., Ehrlich, P.E., Global Lorentzian geometry, Monographs and Textbooks in Pure and Applied Mathematics, 67. Marcel Dekker, New York, 1981.

Lightlike Hypersurfaces of an Indefinite Para Sasakian Manifold

Yıl 2019, Cilt: 9 Sayı: 2, 352 - 373, 30.12.2019
https://doi.org/10.37094/adyujsci.516251

Öz

   In this paper, we initiate the study of lightlike hypersurfaces of an indefinite almost paracontact metric manifold which are tangent to the structure vector field. In particular, we give definitions of invariant lightlike hypersurfaces and screen semi-invariant lightlike hypersurfaces, and give some examples. Integrability conditions for the distributions involved in the screen semi-invariant lightlike hypersurface of an indefinite para Sasakian manifold are investigated.

Kaynakça

  • [1] Küpeli, D.N., On null submanifolds in spacetimes, Geometriae Dedicata, 23(1), 33-51, 1987.
  • [2] Bejancu, A., Duggal, K.L., Real hypersurfaces of indefinite Kaehler manifolds, International Journal of Mathematics and Mathematical Sciences, 16(3), 545-556, 1993.
  • [3] Duggal, K.L., Şahin, B., Differential geometry of lightlike submanifolds, Frontiers in Mathematics. Birkhäuser Verlag, Basel, 2010.
  • [4] Sasaki, S., On differentiable manifolds with certain structures which are closely related to almost contact structure , Tohoku Mathematical Journal, (2) 12, 459-476, 1960.
  • [5] Blair, D.E., Riemannian geometry of contact and symplectic manifolds (Second edition) Progress in Mathematics, 203. Birkhauser Boston, Inc., Boston, MA, 2010.
  • [6] Sato, I., On a structure similar to the almost contact structure, Tensor (N.S.), 30(3), 219-224, 1976.
  • [7] Takahashi, T., Sasakian manifold with pseudo-Riemannian metric, Tohoku Mathematical Journal, 21(2), 271-290, 1969.
  • [8] Duggal, K.L., Bejancu, A., Lightlike submanifolds of semi-Riemannian manifolds and its applications, Mathematics and its Applications, 364. Kluwer Academic Publishers Group, Dordrecht, 1996.
  • [9] Duggal, K.L., Space time manifolds and contact structures, International Journal of Mathematics and Mathematical Sciences, 13(3), 545-553, 1990.
  • [10] Duggal, K.L., Şahin, B., Lightlike submanifolds of indefinite Sasakian manifolds, International Journal of Mathematics and Mathematical Sciences, Art. ID 57585, 21 pp., 2007.
  • [11] Kang, T.H., Jung, S.D., Kim, B.H., Pak, H.K., Pak, J.S., Lightlike hypersurfaces of indefinite Sasakian manifolds, Indian Journal of Pure and Applied Mathematics, 34 (9), 1369-1380, 2003.
  • [12] Matsumoto, K., On Lorentzian paracontact manifolds, Bullet in of the Yamagata University, Natural Science, 12(2), 151-156, 1989.
  • [13] Tripathi, M.M., Kılıç, E., Yüksel Perktaş, S., Keleş, S., Indefinite almost paracontact metric manifolds, International Journal of Mathematics and Mathematical Sciences, Art. Id. 846195, pp. 19, 2010.
  • [14] Yüksel Perktaş, S., Kılıç, E., Tripathi, M.M., Keleş, S., On indefinite - para Sasakian -manifolds, International Journal of Pure and Applied Mathematics, 77(4), 485-499, 2012.
  • [15] Shukla, S.S., Yadev, A., Radical transversal lightlike submanifolds of indefinite para-Sasakian manifolds, Demonstratio Mathematica, vol. XVLVII, No. 4, 994-1011, 2014.
  • [16] Shukla, S.S., Yadev, A., Lightlike submanifolds of indefinite para-Sasakian manifolds, Matematicki Vesnik, 66 (4), 371-386, 2014.
  • [17] O’Neill, B., Semi-Riemannian geometry with applications to relativity, Pure and Applied Mathematics, 103. Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York, 1983.
  • [18] Duggal, K.L., Jin, D.H., Null Curves and Hypersurfaces of Semi-Riemannian Manifolds, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2007.
  • [19] Beem, J.K., Ehrlich, P.E., Global Lorentzian geometry, Monographs and Textbooks in Pure and Applied Mathematics, 67. Marcel Dekker, New York, 1981.
Toplam 19 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

Selcen Yüksel Perktaş 0000-0002-8848-0621

Erol Kılıç

Mukut Mani Tripathi

Yayımlanma Tarihi 30 Aralık 2019
Gönderilme Tarihi 22 Ocak 2019
Kabul Tarihi 19 Aralık 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 9 Sayı: 2

Kaynak Göster

APA Yüksel Perktaş, S., Kılıç, E., & Tripathi, M. M. (2019). Lightlike Hypersurfaces of an Indefinite Para Sasakian Manifold. Adıyaman University Journal of Science, 9(2), 352-373. https://doi.org/10.37094/adyujsci.516251
AMA Yüksel Perktaş S, Kılıç E, Tripathi MM. Lightlike Hypersurfaces of an Indefinite Para Sasakian Manifold. ADYU J SCI. Aralık 2019;9(2):352-373. doi:10.37094/adyujsci.516251
Chicago Yüksel Perktaş, Selcen, Erol Kılıç, ve Mukut Mani Tripathi. “Lightlike Hypersurfaces of an Indefinite Para Sasakian Manifold”. Adıyaman University Journal of Science 9, sy. 2 (Aralık 2019): 352-73. https://doi.org/10.37094/adyujsci.516251.
EndNote Yüksel Perktaş S, Kılıç E, Tripathi MM (01 Aralık 2019) Lightlike Hypersurfaces of an Indefinite Para Sasakian Manifold. Adıyaman University Journal of Science 9 2 352–373.
IEEE S. Yüksel Perktaş, E. Kılıç, ve M. M. Tripathi, “Lightlike Hypersurfaces of an Indefinite Para Sasakian Manifold”, ADYU J SCI, c. 9, sy. 2, ss. 352–373, 2019, doi: 10.37094/adyujsci.516251.
ISNAD Yüksel Perktaş, Selcen vd. “Lightlike Hypersurfaces of an Indefinite Para Sasakian Manifold”. Adıyaman University Journal of Science 9/2 (Aralık 2019), 352-373. https://doi.org/10.37094/adyujsci.516251.
JAMA Yüksel Perktaş S, Kılıç E, Tripathi MM. Lightlike Hypersurfaces of an Indefinite Para Sasakian Manifold. ADYU J SCI. 2019;9:352–373.
MLA Yüksel Perktaş, Selcen vd. “Lightlike Hypersurfaces of an Indefinite Para Sasakian Manifold”. Adıyaman University Journal of Science, c. 9, sy. 2, 2019, ss. 352-73, doi:10.37094/adyujsci.516251.
Vancouver Yüksel Perktaş S, Kılıç E, Tripathi MM. Lightlike Hypersurfaces of an Indefinite Para Sasakian Manifold. ADYU J SCI. 2019;9(2):352-73.

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