Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2019, Cilt: 7 Sayı: 1, 140 - 145, 15.04.2019

Öz

Kaynakça

  • [1] A. Bejancu, CR-submanifolds of a Kahler manifold. I. Proc. Amer. Math. Soc. 1978, 69 (1), 135–142. doi:10.1090/S0002-9939-1978-0467630-0.
  • [2] A. Bejancu and N. Papaghiuc, Semi-invariant submanifolds of a Sasakian manifold. An St Univ Al I Cuza Iasi supl 1981; XVII 1 I-a : 163-170.
  • [3] B. H. Kim, Fibred Riemannian spaces with quasi-Sasakian structure, Hiroshima Math. J. 20, 477–513, 1990.
  • [4] B. Sahin, Nonexistence of warped products semi-slant submanifolds of Kaehler manifolds, Geometriae Dedicata. 117 (2006) 195-202.
  • [5] B. Y. Chen, Geometry of warped product CR-submanifolds in Kaehler manifolds I, K. Monatsh. Math. 133(2001), 177-195.
  • [6] B. Y. Chen, Geometry of warped product CR-Submanifolds in Kaehler Manifolds II, Monatsh. Math. 134 (2001) 103-119.
  • [7] B. Y. Chen and M. I. Munteanu, Geometry of PR-warped products in para-Kaehler manifolds, Taiwan. J. Math., 16 (2012), 1293-1327.
  • [8] D. E. Blair, The theory of quasi-Sasakian structure, J. Differential Geo. 1, 331-345, 1967.
  • [9] I. Hasegawa and I. Mihai, Contact CR-warped product submanifolds in Sasakian manifolds, Geom. Dedicata, 102 (2003), 143-150.
  • [10] J. A. Oubina, New classes of almost contact metric structures, Publ. Math. Debrecen 32, 187–193, 1985.
  • [11] J. C. Gonzalez, and D. Chinea, Quasi-Sasakian homogeneous structures on the generalized Heisenberg group H(p, 1), Proc. Amer. Math. Soc. 105, 173–184, 1989.
  • [12] K. Arslan, R. Ezentas, I. Mihai and C. Murathan, Contact CR-warped product submanifolds in Kenmotsu space forms, J. Korean Math. Soc., 42 (2005), 1101-1110.
  • [13] R. L. Bishop and B. O. Neill, Manifolds of negative curvature, Trans. Amer. Math. Soc., 145 (1969), 1-49.
  • [14] S. Hiepko, Eine inner kennzeichungder verzerrten produkte, Math. Ann., 241 (1979), 209-215.
  • [15] S. Kanemaki, Quasi-Sasakian manifolds, Tohoku Math. J. 29, 227–233, 1977.
  • [16] S. Kanemaki, On quasi-Sasakian manifolds, Differential Geometry Banach Center Publications 12, 95–125, 1984.
  • [17] S. Rahman and Shafiullah, Geometry of Hypersurfaces of a Semi Symmetric Semi Metric Connection in a Quasi-Sasakian Manifold. Journal of Purvanchal Academy of Sciences, Vol. 17 (2011) pp. 231-242.
  • [18] S. Rahman and A. Ahmad, On The Geometry of Hypersurfaces of a Certain Connection in a Quasi-Sasakian Manifold, International Journal Mathematical Combinatorics Vol.3 (2011), pp. 23-33.
  • [19] S. Rahman, Some Properties of Hyperbolic contact Manifold in a Quasi Sasakian Manifold, Turkic World Mathematical Society Journal of Applied and Engineering Mathematics Vol. 1 No. 1, (2011), pp. 41-48.
  • [20] S. Rahman, Geometry of Hypersurfaces of a semi symmetric metric connection in a quasi-Sasakian manifold, Journal-Proceedings of the Institute of Applied Mathematics, Vol.3 No.2 (2014), pp.152-164.
  • [21] S. Rahman, Geometry of hypersurfaces of a quarter semi symmetric non metric connection in a quasi-Sasakian manifold. Carpathian Mathematical Publications Vol. 7(2) (2015) pp. 226-235 doi:10.15330/cmp.7.2.226-235.
  • [22] S. Rahman and N. K. Agrawal, On the geometry of slant and pseudo-slant submanifolds in a quasi Sasakian manifolds, J. Modern Technology and Engineering Vol. 2, No.1, 2017, pp.82-89.
  • [23] S. Rahman, Contact conformal connection on a geometry of hypersurfaces with certain connection in a quasi-Sasakian manifold, Bulletin of the Transilvania University of Brasov Series III: Mathematics, Informatics, Physics, Vol 10 (59), No. 1, 2017 pp.135-148.
  • [24] S. Tanno, Quasi-Sasakian structure of rank 2p + 1, J. Differential Geom. 5, 317–324, 1971.

Contact Cr-Warped Product Submanifolds of Nearly Quasi-Sasakian Manifold

Yıl 2019, Cilt: 7 Sayı: 1, 140 - 145, 15.04.2019

Öz



In the present
paper, we construct contact CR-warped product submanifolds of nearly quasi
Sasakian manifold. We have obtained results on the existence of warped product
CR Submanifolds of nearly quasi Sasakian manifold and discuss the
characterization result. We also construct the inequality
 for contact CR warped products of nearly quasi
Sasakian manifolds. The equality cases are also discussed.





Kaynakça

  • [1] A. Bejancu, CR-submanifolds of a Kahler manifold. I. Proc. Amer. Math. Soc. 1978, 69 (1), 135–142. doi:10.1090/S0002-9939-1978-0467630-0.
  • [2] A. Bejancu and N. Papaghiuc, Semi-invariant submanifolds of a Sasakian manifold. An St Univ Al I Cuza Iasi supl 1981; XVII 1 I-a : 163-170.
  • [3] B. H. Kim, Fibred Riemannian spaces with quasi-Sasakian structure, Hiroshima Math. J. 20, 477–513, 1990.
  • [4] B. Sahin, Nonexistence of warped products semi-slant submanifolds of Kaehler manifolds, Geometriae Dedicata. 117 (2006) 195-202.
  • [5] B. Y. Chen, Geometry of warped product CR-submanifolds in Kaehler manifolds I, K. Monatsh. Math. 133(2001), 177-195.
  • [6] B. Y. Chen, Geometry of warped product CR-Submanifolds in Kaehler Manifolds II, Monatsh. Math. 134 (2001) 103-119.
  • [7] B. Y. Chen and M. I. Munteanu, Geometry of PR-warped products in para-Kaehler manifolds, Taiwan. J. Math., 16 (2012), 1293-1327.
  • [8] D. E. Blair, The theory of quasi-Sasakian structure, J. Differential Geo. 1, 331-345, 1967.
  • [9] I. Hasegawa and I. Mihai, Contact CR-warped product submanifolds in Sasakian manifolds, Geom. Dedicata, 102 (2003), 143-150.
  • [10] J. A. Oubina, New classes of almost contact metric structures, Publ. Math. Debrecen 32, 187–193, 1985.
  • [11] J. C. Gonzalez, and D. Chinea, Quasi-Sasakian homogeneous structures on the generalized Heisenberg group H(p, 1), Proc. Amer. Math. Soc. 105, 173–184, 1989.
  • [12] K. Arslan, R. Ezentas, I. Mihai and C. Murathan, Contact CR-warped product submanifolds in Kenmotsu space forms, J. Korean Math. Soc., 42 (2005), 1101-1110.
  • [13] R. L. Bishop and B. O. Neill, Manifolds of negative curvature, Trans. Amer. Math. Soc., 145 (1969), 1-49.
  • [14] S. Hiepko, Eine inner kennzeichungder verzerrten produkte, Math. Ann., 241 (1979), 209-215.
  • [15] S. Kanemaki, Quasi-Sasakian manifolds, Tohoku Math. J. 29, 227–233, 1977.
  • [16] S. Kanemaki, On quasi-Sasakian manifolds, Differential Geometry Banach Center Publications 12, 95–125, 1984.
  • [17] S. Rahman and Shafiullah, Geometry of Hypersurfaces of a Semi Symmetric Semi Metric Connection in a Quasi-Sasakian Manifold. Journal of Purvanchal Academy of Sciences, Vol. 17 (2011) pp. 231-242.
  • [18] S. Rahman and A. Ahmad, On The Geometry of Hypersurfaces of a Certain Connection in a Quasi-Sasakian Manifold, International Journal Mathematical Combinatorics Vol.3 (2011), pp. 23-33.
  • [19] S. Rahman, Some Properties of Hyperbolic contact Manifold in a Quasi Sasakian Manifold, Turkic World Mathematical Society Journal of Applied and Engineering Mathematics Vol. 1 No. 1, (2011), pp. 41-48.
  • [20] S. Rahman, Geometry of Hypersurfaces of a semi symmetric metric connection in a quasi-Sasakian manifold, Journal-Proceedings of the Institute of Applied Mathematics, Vol.3 No.2 (2014), pp.152-164.
  • [21] S. Rahman, Geometry of hypersurfaces of a quarter semi symmetric non metric connection in a quasi-Sasakian manifold. Carpathian Mathematical Publications Vol. 7(2) (2015) pp. 226-235 doi:10.15330/cmp.7.2.226-235.
  • [22] S. Rahman and N. K. Agrawal, On the geometry of slant and pseudo-slant submanifolds in a quasi Sasakian manifolds, J. Modern Technology and Engineering Vol. 2, No.1, 2017, pp.82-89.
  • [23] S. Rahman, Contact conformal connection on a geometry of hypersurfaces with certain connection in a quasi-Sasakian manifold, Bulletin of the Transilvania University of Brasov Series III: Mathematics, Informatics, Physics, Vol 10 (59), No. 1, 2017 pp.135-148.
  • [24] S. Tanno, Quasi-Sasakian structure of rank 2p + 1, J. Differential Geom. 5, 317–324, 1971.
Toplam 24 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Articles
Yazarlar

Shamsur Rahman 0000-0003-0995-2860

Mohd Sadiq Khan Bu kişi benim

Aboo Horaira Bu kişi benim

Yayımlanma Tarihi 15 Nisan 2019
Gönderilme Tarihi 13 Haziran 2018
Kabul Tarihi 15 Şubat 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 7 Sayı: 1

Kaynak Göster

APA Rahman, S., Khan, M. S., & Horaira, A. (2019). Contact Cr-Warped Product Submanifolds of Nearly Quasi-Sasakian Manifold. Konuralp Journal of Mathematics, 7(1), 140-145.
AMA Rahman S, Khan MS, Horaira A. Contact Cr-Warped Product Submanifolds of Nearly Quasi-Sasakian Manifold. Konuralp J. Math. Nisan 2019;7(1):140-145.
Chicago Rahman, Shamsur, Mohd Sadiq Khan, ve Aboo Horaira. “Contact Cr-Warped Product Submanifolds of Nearly Quasi-Sasakian Manifold”. Konuralp Journal of Mathematics 7, sy. 1 (Nisan 2019): 140-45.
EndNote Rahman S, Khan MS, Horaira A (01 Nisan 2019) Contact Cr-Warped Product Submanifolds of Nearly Quasi-Sasakian Manifold. Konuralp Journal of Mathematics 7 1 140–145.
IEEE S. Rahman, M. S. Khan, ve A. Horaira, “Contact Cr-Warped Product Submanifolds of Nearly Quasi-Sasakian Manifold”, Konuralp J. Math., c. 7, sy. 1, ss. 140–145, 2019.
ISNAD Rahman, Shamsur vd. “Contact Cr-Warped Product Submanifolds of Nearly Quasi-Sasakian Manifold”. Konuralp Journal of Mathematics 7/1 (Nisan 2019), 140-145.
JAMA Rahman S, Khan MS, Horaira A. Contact Cr-Warped Product Submanifolds of Nearly Quasi-Sasakian Manifold. Konuralp J. Math. 2019;7:140–145.
MLA Rahman, Shamsur vd. “Contact Cr-Warped Product Submanifolds of Nearly Quasi-Sasakian Manifold”. Konuralp Journal of Mathematics, c. 7, sy. 1, 2019, ss. 140-5.
Vancouver Rahman S, Khan MS, Horaira A. Contact Cr-Warped Product Submanifolds of Nearly Quasi-Sasakian Manifold. Konuralp J. Math. 2019;7(1):140-5.
Creative Commons License
The published articles in KJM are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.