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

Year 2025, Volume: 54 Issue: 1, 200 - 212, 28.02.2025
https://doi.org/10.15672/hujms.1211053

Abstract

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.

References

  • [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.
Year 2025, Volume: 54 Issue: 1, 200 - 212, 28.02.2025
https://doi.org/10.15672/hujms.1211053

Abstract

References

  • [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.
There are 33 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Prınce Majeed 0000-0002-4425-1413

Mehraj Lone 0000-0002-4764-9224

Early Pub Date April 14, 2024
Publication Date February 28, 2025
Published in Issue Year 2025 Volume: 54 Issue: 1

Cite

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. February 2025;54(1):200-212. doi:10.15672/hujms.1211053
Chicago Majeed, Prınce, and Mehraj Lone. “Warped Product Pointwise Bi-Slant Submanifolds of Locally Product Riemannian Manifolds”. Hacettepe Journal of Mathematics and Statistics 54, no. 1 (February 2025): 200-212. https://doi.org/10.15672/hujms.1211053.
EndNote Majeed P, Lone M (February 1, 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 and M. Lone, “Warped product pointwise bi-slant submanifolds of locally product Riemannian manifolds”, Hacettepe Journal of Mathematics and Statistics, vol. 54, no. 1, pp. 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 (February 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 and Mehraj Lone. “Warped Product Pointwise Bi-Slant Submanifolds of Locally Product Riemannian Manifolds”. Hacettepe Journal of Mathematics and Statistics, vol. 54, no. 1, 2025, pp. 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.