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Warped product pointwise bi-slant submanifolds of locally product Riemannian manifolds

Yıl 2025, , 200 - 212, 28.02.2025

Prınce Majeed , Mehraj Lone

https://doi.org/10.15672/hujms.1211053
Cited By: 1

Öz

In this paper we introduce the concept of pointwise bi-slant submanifolds of locally product Riemannian manifolds and studied warped product pointwise bi-slant submanifolds of locally product Riemannian manifolds. We obtain some characterization results for warped products pointwise bi-slant submanifolds. Also, we provide some non-trivial examples of such warped product submanifolds.

Anahtar Kelimeler

locally product Riemannian manifold pointwise bi-slant submanifolds Warped products

Kaynakça

  • [1] F. R. Al-Solamy, V. A. Khan and S. Uddin, Geometry of warped product semi-slant submanifolds of nearly Kaehler manifolds, Results in Mathematics. 71(3), 783-799, 2017.
  • [2] M. Atceken, Warped product semi-slant submanifolds in locally Riemannian product manifolds, Bull. Aust. Math. Soc. 77(2), 177-186, 2008.
  • [3] M. Atçeken, Slant submanifolds of a Riemannian product manifold, Acta Math. Sci. Ser B Engl. Ed. 30(1), 215-224, 2010.
  • [4] A. Bejancu, Semi-invariant submanifolds of locally product Riemannian manifolds, An. Univ. Timisoara. Ser Stiint. Math. 22, 3-11, 1984.
  • [5] R. L. Bishop and B. O’Neill, Manifolds of negative curvature, Trans. Am. Math. Soc. 145, 1-49, 1969.
  • [6] J. L. Cabrerizo, A. Carriazo, L.M. Fernandez and M. Fernandez, Semi-Slant submanifolds of a Sasakian manifold, Geom. Dedicata. 78(2), 183-199, 1999.
  • [7] B. Y. Chen, Slant immersions, Bull. Aust, Math. Soc. 41(1), 135-147, 1990.
  • [8] B. Y. Chen, Geometry of warped product CR-submanifolds in Kaehler manifolds, Monatsh. Math. 133, 177-195, 2001.
  • [9] B. Y. Chen, Geometry of warped product CR-submanifolds in Kaehler manifolds II, Monatsh. Math. 134, 103-119, 2001.
  • [10] B. Y. Chen, Another general inequality for CR-warped products in complex space forms, Hokkaido Math. J. 32(2), 415-444, 2003.
  • [11] B. Y. Chen, CR-warped products in complex projective spaces with compact holomorphic factor, Monatshefte für Mathematik. 141(3), 177-186, 2004.
  • [12] B. Y. Chen, Geometry of warped product submanifolds: A survey, J. Adv. Math. Stud. 6(2), 1-8, 2013.
  • [13] B. Y. Chen, Differential geometry of warped product manifolds and submanifolds, World Scientific. 2017.
  • [14] B. Y. Chen and O. J. Garay, Pointwise slant submanifolds in almost Hermitian manifolds, Turk. J. Math. 36, 630-640, 2012.
  • [15] B. Y. Chen, M. H. Shahid and F. R. Al-Solamy, Complex Geometry of Slant Submanifolds, Springer. Berlin 2021.
  • [16] B. Y. Chen and S. Uddin, Warped product pointwise bi-slant submanifolds of Kaehler manifolds, Publicationes Mathematicae. 92(1-2), 183-199, 2018.
  • [17] F. Etayo, On quasi-slant submanifolds of an almost Hermitian manifold, Publ. Math. Debrecen. 53(1-2), 217-223, 1998.
  • [18] M. Gülbahar, E. Kilic and S. S. ÇELK Special proper pointwise slant surfaces of a locally product Riemannian manifold, Turk. J. Math. 39(6), 884-899, 2015.
  • [19] S. Hiepko, Eine inner kennzeichungder verzerrten produkte, Math. Ann. 241, 209-215, 1979.
  • [20] Y. Kentaro and M. Kon, Generic submanifolds, Annali di Matematica Pura ed Applicata. 123(1), 59-92, 1980.
  • [21] V. A. Khan and M. A. Khan, Semi-slant submanifolds of a nearly Kaehler manifold, Turk. J. Math. 31(4), 341-353, 2007.
  • [22] H. Li and X. Liu, Semi-slant submanifolds of a locally product manifold, Georgian Math. J. 12, 273-282, 2005.
  • [23] M. A. Lone, M. H. Shahid and S. D. Sharma, Hemi-slant submanifolds of nearly Kaehler manifolds, Gulf Journal of Mathematics, 4(3), 2016.
  • [24] M. F. Naghi, M. S. Stankovic and F. Alghamdi, Chens improved inequality for pointwise hemi-slant warped products in Kaehler manifolds, Filomat. 34(3), 807-814, 2020.
  • [25] N. Papaghuic, Semi-slant submanifolds of a Kahlerian manifold, An. Stiint. Univ. Al. I. Cuza Iasi Mat. 40(1), 55-61, 1994.
  • [26] B. Sahin, Slant submanifolds of an almost product Riemannian manifold, J. Korean Math. Soc. 43(4), 717-732, 2006.
  • [27] B. Sahin, Non-existence of warped product semi-slant submanifolds of Kaehler manifolds, Geometriae Dedicata. 117(1), 195-202, 2006.
  • [28] B. Sahin, Warped product semi-slant submanifolds of a locally product Riemannian manifold, Studia. Sci. Math. Hungar. 46(2), 169-184, 2009.
  • [29] B. Sahin, Warped product pointwise semi-slant submanifolds of Kaehler manifolds, Port. Math. 70, 252-268, 2013.
  • [30] B. Sahin and M. Atceken, Semi-invariant submanifolds of Riemannian product manifold, Balkan J. Geom. Appl. 8(1), 91-100, 2003.
  • [31] S. Uddin, F. Alghamdi and F. R. Al-Solamy, Geometry of warped product pointwise semi-slant submanifolds of locally product Riemannian manifolds, Journal of Geometry and Physics. 152, 103658, 2020.
  • [32] S. Uddin, B. Y. Chen and F. R. Al-Solamy, Warped product bi-slant immersions in Kaehler manifolds, Mediterr. J. Math. 14(2), 14-95, 2017.
  • [33] K. Yano and M. Kon, Structures on manifolds, Series in Pure mathematics, World scientific Publishing Co. Singapore, 1984.

Yıl 2025, , 200 - 212, 28.02.2025

Prınce Majeed , Mehraj Lone

https://doi.org/10.15672/hujms.1211053
Cited By: 1

Öz

Anahtar Kelimeler

Locally product Riemannian manifold Pointwise bi-slant submanifolds Warped products

Kaynakça

  • [1] F. R. Al-Solamy, V. A. Khan and S. Uddin, Geometry of warped product semi-slant submanifolds of nearly Kaehler manifolds, Results in Mathematics. 71(3), 783-799, 2017.
  • [2] M. Atceken, Warped product semi-slant submanifolds in locally Riemannian product manifolds, Bull. Aust. Math. Soc. 77(2), 177-186, 2008.
  • [3] M. Atçeken, Slant submanifolds of a Riemannian product manifold, Acta Math. Sci. Ser B Engl. Ed. 30(1), 215-224, 2010.
  • [4] A. Bejancu, Semi-invariant submanifolds of locally product Riemannian manifolds, An. Univ. Timisoara. Ser Stiint. Math. 22, 3-11, 1984.
  • [5] R. L. Bishop and B. O’Neill, Manifolds of negative curvature, Trans. Am. Math. Soc. 145, 1-49, 1969.
  • [6] J. L. Cabrerizo, A. Carriazo, L.M. Fernandez and M. Fernandez, Semi-Slant submanifolds of a Sasakian manifold, Geom. Dedicata. 78(2), 183-199, 1999.
  • [7] B. Y. Chen, Slant immersions, Bull. Aust, Math. Soc. 41(1), 135-147, 1990.
  • [8] B. Y. Chen, Geometry of warped product CR-submanifolds in Kaehler manifolds, Monatsh. Math. 133, 177-195, 2001.
  • [9] B. Y. Chen, Geometry of warped product CR-submanifolds in Kaehler manifolds II, Monatsh. Math. 134, 103-119, 2001.
  • [10] B. Y. Chen, Another general inequality for CR-warped products in complex space forms, Hokkaido Math. J. 32(2), 415-444, 2003.
  • [11] B. Y. Chen, CR-warped products in complex projective spaces with compact holomorphic factor, Monatshefte für Mathematik. 141(3), 177-186, 2004.
  • [12] B. Y. Chen, Geometry of warped product submanifolds: A survey, J. Adv. Math. Stud. 6(2), 1-8, 2013.
  • [13] B. Y. Chen, Differential geometry of warped product manifolds and submanifolds, World Scientific. 2017.
  • [14] B. Y. Chen and O. J. Garay, Pointwise slant submanifolds in almost Hermitian manifolds, Turk. J. Math. 36, 630-640, 2012.
  • [15] B. Y. Chen, M. H. Shahid and F. R. Al-Solamy, Complex Geometry of Slant Submanifolds, Springer. Berlin 2021.
  • [16] B. Y. Chen and S. Uddin, Warped product pointwise bi-slant submanifolds of Kaehler manifolds, Publicationes Mathematicae. 92(1-2), 183-199, 2018.
  • [17] F. Etayo, On quasi-slant submanifolds of an almost Hermitian manifold, Publ. Math. Debrecen. 53(1-2), 217-223, 1998.
  • [18] M. Gülbahar, E. Kilic and S. S. ÇELK Special proper pointwise slant surfaces of a locally product Riemannian manifold, Turk. J. Math. 39(6), 884-899, 2015.
  • [19] S. Hiepko, Eine inner kennzeichungder verzerrten produkte, Math. Ann. 241, 209-215, 1979.
  • [20] Y. Kentaro and M. Kon, Generic submanifolds, Annali di Matematica Pura ed Applicata. 123(1), 59-92, 1980.
  • [21] V. A. Khan and M. A. Khan, Semi-slant submanifolds of a nearly Kaehler manifold, Turk. J. Math. 31(4), 341-353, 2007.
  • [22] H. Li and X. Liu, Semi-slant submanifolds of a locally product manifold, Georgian Math. J. 12, 273-282, 2005.
  • [23] M. A. Lone, M. H. Shahid and S. D. Sharma, Hemi-slant submanifolds of nearly Kaehler manifolds, Gulf Journal of Mathematics, 4(3), 2016.
  • [24] M. F. Naghi, M. S. Stankovic and F. Alghamdi, Chens improved inequality for pointwise hemi-slant warped products in Kaehler manifolds, Filomat. 34(3), 807-814, 2020.
  • [25] N. Papaghuic, Semi-slant submanifolds of a Kahlerian manifold, An. Stiint. Univ. Al. I. Cuza Iasi Mat. 40(1), 55-61, 1994.
  • [26] B. Sahin, Slant submanifolds of an almost product Riemannian manifold, J. Korean Math. Soc. 43(4), 717-732, 2006.
  • [27] B. Sahin, Non-existence of warped product semi-slant submanifolds of Kaehler manifolds, Geometriae Dedicata. 117(1), 195-202, 2006.
  • [28] B. Sahin, Warped product semi-slant submanifolds of a locally product Riemannian manifold, Studia. Sci. Math. Hungar. 46(2), 169-184, 2009.
  • [29] B. Sahin, Warped product pointwise semi-slant submanifolds of Kaehler manifolds, Port. Math. 70, 252-268, 2013.
  • [30] B. Sahin and M. Atceken, Semi-invariant submanifolds of Riemannian product manifold, Balkan J. Geom. Appl. 8(1), 91-100, 2003.
  • [31] S. Uddin, F. Alghamdi and F. R. Al-Solamy, Geometry of warped product pointwise semi-slant submanifolds of locally product Riemannian manifolds, Journal of Geometry and Physics. 152, 103658, 2020.
  • [32] S. Uddin, B. Y. Chen and F. R. Al-Solamy, Warped product bi-slant immersions in Kaehler manifolds, Mediterr. J. Math. 14(2), 14-95, 2017.
  • [33] K. Yano and M. Kon, Structures on manifolds, Series in Pure mathematics, World scientific Publishing Co. Singapore, 1984.
Toplam 33 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

Prınce Majeed 0000-0002-4425-1413

Mehraj Lone 0000-0002-4764-9224

Erken Görünüm Tarihi 14 Nisan 2024
Yayımlanma Tarihi 28 Şubat 2025
Yayımlandığı Sayı Yıl 2025

Kaynak Göster

APA Majeed, P., & Lone, M. (2025). Warped product pointwise bi-slant submanifolds of locally product Riemannian manifolds. Hacettepe Journal of Mathematics and Statistics, 54(1), 200-212. https://doi.org/10.15672/hujms.1211053
AMA Majeed P, Lone M. Warped product pointwise bi-slant submanifolds of locally product Riemannian manifolds. Hacettepe Journal of Mathematics and Statistics. Şubat 2025;54(1):200-212. doi:10.15672/hujms.1211053
Chicago Majeed, Prınce, ve Mehraj Lone. “Warped Product Pointwise Bi-Slant Submanifolds of Locally Product Riemannian Manifolds”. Hacettepe Journal of Mathematics and Statistics 54, sy. 1 (Şubat 2025): 200-212. https://doi.org/10.15672/hujms.1211053.
EndNote Majeed P, Lone M (01 Şubat 2025) Warped product pointwise bi-slant submanifolds of locally product Riemannian manifolds. Hacettepe Journal of Mathematics and Statistics 54 1 200–212.
IEEE P. Majeed ve M. Lone, “Warped product pointwise bi-slant submanifolds of locally product Riemannian manifolds”, Hacettepe Journal of Mathematics and Statistics, c. 54, sy. 1, ss. 200–212, 2025, doi: 10.15672/hujms.1211053.
ISNAD Majeed, Prınce - Lone, Mehraj. “Warped Product Pointwise Bi-Slant Submanifolds of Locally Product Riemannian Manifolds”. Hacettepe Journal of Mathematics and Statistics 54/1 (Şubat 2025), 200-212. https://doi.org/10.15672/hujms.1211053.
JAMA Majeed P, Lone M. Warped product pointwise bi-slant submanifolds of locally product Riemannian manifolds. Hacettepe Journal of Mathematics and Statistics. 2025;54:200–212.
MLA Majeed, Prınce ve Mehraj Lone. “Warped Product Pointwise Bi-Slant Submanifolds of Locally Product Riemannian Manifolds”. Hacettepe Journal of Mathematics and Statistics, c. 54, sy. 1, 2025, ss. 200-12, doi:10.15672/hujms.1211053.
Vancouver Majeed P, Lone M. Warped product pointwise bi-slant submanifolds of locally product Riemannian manifolds. Hacettepe Journal of Mathematics and Statistics. 2025;54(1):200-12.

Cited By

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https://doi.org/10.1007/s11565-024-00565-x

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