Research Article
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Year 2024, Volume: 17 Issue: 2, 348 - 357

Idrees Harry , Mehraj Lone

https://doi.org/10.36890/iejg.1329607

Abstract

References

  • [1] Atceken, A.: Slant submanifolds of a Riemannian product manifold. Acta Mathematica Scientia B. 30(1), 215-224 (2010).
  • [2] Atceken, M., Dirik, S.: Pseudo-slant submanifolds of a locally decomposable Riemannian manifold. J. Adv. Math. 11(8), 5587-5599 (2015).
  • [3] Alegre, P., Carriazo, A.: Slant submanifolds of para-Hermitian manifolds. Mediterr. J. Math. 14(5), 1-14 (2017).
  • [4] Blaga, A. M., Hretcanu, C. E.: Golden warped product Riemannian manifolds. Lib. Math. 37(2), 39-49 (2017).
  • [5] Blaga, A. M., Hretcanu, C. E.: Invariant, anti-invariant and slant submanifolds of a metallic Riemannian manifold. Novi Sad J. Math. 48(2), 55-80 (2018).
  • [6] Chen, B. Y.: Geometry of Slant Submanifolds. Katholieke Universiteit Leuven, Leuven, Belgium. 1990.
  • [7] Chen, B. Y.: Slant immersions. BulL. Aus. Math. Soc. 41(1), 135–147 (1990).
  • [8] Crasmareanu, M., Hre¸tcanu, C. E.: Metallic differential geometry. Chaos Solitons Fractals. 38(5), 1229-1238 (2008).
  • [9] Crasmareanu, M., Hretcanu, C. E., Munteanu, M. I.: Golden- and product-shaped hypersurfaces in real space forms. Int. J. Geom. Methods Mod. Phys. 10(4), Article ID 1320006, 2013.
  • [10] Carriazo, A.: Bi-slant immersions. Proc ICRAMS. 55, 88-97 (2000).
  • [11] Choudhary, M. A., Park, K. S.: Optimization on slant submanifolds of golden Riemannian manifolds using generalized normalized δ-Casorati curvatures. J. Geom. 111, 31 (2020). https://doi.org/10.1007/s00022-020-00544-5.
  • [12] Choudhary, M. A., Blaga, A. M.: Inequalities for generalized normalized δ-Casorati curvatures of slant submanifolds in metallic Riemannian space forms. J. Geom. 111, 39 (2020). https://doi.org/10.1007/s00022-020-00552-5.
  • [13] Choudhary, M.A., Blaga, A. M.: Generalized Wintgen inequality for slant submanifolds in metallic Riemannian space forms. J. Geom. 112, 26 (2021). https://doi.org/10.1007/s00022-021-00590-7.
  • [14] Etayo, F., Santamaria, R., Upadhyay, A.: “On the geometry of almost Golden Riemannian manifolds. Mediterr. J. Math. 14(5), 1-14 (2017).
  • [15] Gezer A., Cengiz, N., Salimov, A.: On integrability of golden Riemannian structures. Turk. J. Math. 37(4), 693-703 (2013).
  • [16] Goldberg, S. I., Yano, K.: Polynomial structures on manifolds. Kodai Mathematical Seminar Reports. 22, 199-218 (1970).
  • [17] Hretcanu, C. E., Crasmareanu, M.: Metallic structures on Riemannian manifolds. Revista de la Union Matematica Argentina. 54(2), 15-27 (2013).
  • [18] Hretcanu, C. E., Blaga, A. M.: Slant and semi-slant submanifolds in metallic Riemannian manifolds. J. Funct. Spaces. 2864263, 1-13 (2018).
  • [19] Hretcanu, C. E., Blaga A. M.: Hemi-slant submanifolds in metallic riemannian manifolds. Carpathian J. Math. 35(1), 59–68 (2019).
  • [20] Hretcanu, C. E., Blaga, A. M.: Warped product submanifolds of metallic Riemannian manifolds. Tamkang J. Math. 51(3), 161-186 (2020).
  • [21] Lotta, A.: Slant submanifolds in contact geometry. BULL. Math. Soc. Sc. Math. Roumania Tome. 39(1), 183-198 (1996).
  • [22] Papaghiuc, N.: Semi-slant submanifolds of a Kaehlerian manifold. Scientifc Annals of the Alexandru Ioan Cuza University of Iasi, s. I. a, Mathematics. 40(1), 55-61 (1994).
  • [23] Prasad, R., Akyol, M. A., Verma, S. K., Kumar, S.: Quasi bi-slant submanifolds of Kaehler manifolds. Int. Electron. J. Geom. 15(1), 57-68 (2022).
  • [24] Sahin, B.: Slant submanifolds of an almost product Riemannian manifold. J. Korean Math. Soc. 43(4), 2006, 717-732.
  • [25] de Spinadel, V. W.: The metallic means family and forbidden symmetries. Int. Math. J. 2 (3), 279-288 (2002).

Quasi Bi-slant Submanifolds of Locally Metallic Riemannian Manifolds

Year 2024, Volume: 17 Issue: 2, 348 - 357

Idrees Harry , Mehraj Lone

https://doi.org/10.36890/iejg.1329607

Abstract

In this article, we investigate quasi bi-slant submanifolds of locally metallic Riemannian manifolds. The main objective is to determine the conditions under which the distributions used in defining these submanifolds are integrable. We also establish the necessary and sufficient conditions for quasi bi-slant submanifold to be a totally geodesic foliation.

Keywords

Metallic Riemannian manifolds quasi bi-slant submanifolds distribution

References

  • [1] Atceken, A.: Slant submanifolds of a Riemannian product manifold. Acta Mathematica Scientia B. 30(1), 215-224 (2010).
  • [2] Atceken, M., Dirik, S.: Pseudo-slant submanifolds of a locally decomposable Riemannian manifold. J. Adv. Math. 11(8), 5587-5599 (2015).
  • [3] Alegre, P., Carriazo, A.: Slant submanifolds of para-Hermitian manifolds. Mediterr. J. Math. 14(5), 1-14 (2017).
  • [4] Blaga, A. M., Hretcanu, C. E.: Golden warped product Riemannian manifolds. Lib. Math. 37(2), 39-49 (2017).
  • [5] Blaga, A. M., Hretcanu, C. E.: Invariant, anti-invariant and slant submanifolds of a metallic Riemannian manifold. Novi Sad J. Math. 48(2), 55-80 (2018).
  • [6] Chen, B. Y.: Geometry of Slant Submanifolds. Katholieke Universiteit Leuven, Leuven, Belgium. 1990.
  • [7] Chen, B. Y.: Slant immersions. BulL. Aus. Math. Soc. 41(1), 135–147 (1990).
  • [8] Crasmareanu, M., Hre¸tcanu, C. E.: Metallic differential geometry. Chaos Solitons Fractals. 38(5), 1229-1238 (2008).
  • [9] Crasmareanu, M., Hretcanu, C. E., Munteanu, M. I.: Golden- and product-shaped hypersurfaces in real space forms. Int. J. Geom. Methods Mod. Phys. 10(4), Article ID 1320006, 2013.
  • [10] Carriazo, A.: Bi-slant immersions. Proc ICRAMS. 55, 88-97 (2000).
  • [11] Choudhary, M. A., Park, K. S.: Optimization on slant submanifolds of golden Riemannian manifolds using generalized normalized δ-Casorati curvatures. J. Geom. 111, 31 (2020). https://doi.org/10.1007/s00022-020-00544-5.
  • [12] Choudhary, M. A., Blaga, A. M.: Inequalities for generalized normalized δ-Casorati curvatures of slant submanifolds in metallic Riemannian space forms. J. Geom. 111, 39 (2020). https://doi.org/10.1007/s00022-020-00552-5.
  • [13] Choudhary, M.A., Blaga, A. M.: Generalized Wintgen inequality for slant submanifolds in metallic Riemannian space forms. J. Geom. 112, 26 (2021). https://doi.org/10.1007/s00022-021-00590-7.
  • [14] Etayo, F., Santamaria, R., Upadhyay, A.: “On the geometry of almost Golden Riemannian manifolds. Mediterr. J. Math. 14(5), 1-14 (2017).
  • [15] Gezer A., Cengiz, N., Salimov, A.: On integrability of golden Riemannian structures. Turk. J. Math. 37(4), 693-703 (2013).
  • [16] Goldberg, S. I., Yano, K.: Polynomial structures on manifolds. Kodai Mathematical Seminar Reports. 22, 199-218 (1970).
  • [17] Hretcanu, C. E., Crasmareanu, M.: Metallic structures on Riemannian manifolds. Revista de la Union Matematica Argentina. 54(2), 15-27 (2013).
  • [18] Hretcanu, C. E., Blaga, A. M.: Slant and semi-slant submanifolds in metallic Riemannian manifolds. J. Funct. Spaces. 2864263, 1-13 (2018).
  • [19] Hretcanu, C. E., Blaga A. M.: Hemi-slant submanifolds in metallic riemannian manifolds. Carpathian J. Math. 35(1), 59–68 (2019).
  • [20] Hretcanu, C. E., Blaga, A. M.: Warped product submanifolds of metallic Riemannian manifolds. Tamkang J. Math. 51(3), 161-186 (2020).
  • [21] Lotta, A.: Slant submanifolds in contact geometry. BULL. Math. Soc. Sc. Math. Roumania Tome. 39(1), 183-198 (1996).
  • [22] Papaghiuc, N.: Semi-slant submanifolds of a Kaehlerian manifold. Scientifc Annals of the Alexandru Ioan Cuza University of Iasi, s. I. a, Mathematics. 40(1), 55-61 (1994).
  • [23] Prasad, R., Akyol, M. A., Verma, S. K., Kumar, S.: Quasi bi-slant submanifolds of Kaehler manifolds. Int. Electron. J. Geom. 15(1), 57-68 (2022).
  • [24] Sahin, B.: Slant submanifolds of an almost product Riemannian manifold. J. Korean Math. Soc. 43(4), 2006, 717-732.
  • [25] de Spinadel, V. W.: The metallic means family and forbidden symmetries. Int. Math. J. 2 (3), 279-288 (2002).
There are 25 citations in total.

Details

Primary Language English
Subjects Algebraic and Differential Geometry
Journal Section Research Article
Authors

Idrees Harry 0000-0003-3930-2009

Mehraj Lone 0000-0002-4764-9224

Early Pub Date September 16, 2024
Publication Date
Acceptance Date November 9, 2023
Published in Issue Year 2024 Volume: 17 Issue: 2

Cite

APA Harry, I., & Lone, M. (2024). Quasi Bi-slant Submanifolds of Locally Metallic Riemannian Manifolds. International Electronic Journal of Geometry, 17(2), 348-357. https://doi.org/10.36890/iejg.1329607
AMA Harry I, Lone M. Quasi Bi-slant Submanifolds of Locally Metallic Riemannian Manifolds. Int. Electron. J. Geom. September 2024;17(2):348-357. doi:10.36890/iejg.1329607
Chicago Harry, Idrees, and Mehraj Lone. “Quasi Bi-Slant Submanifolds of Locally Metallic Riemannian Manifolds”. International Electronic Journal of Geometry 17, no. 2 (September 2024): 348-57. https://doi.org/10.36890/iejg.1329607.
EndNote Harry I, Lone M (September 1, 2024) Quasi Bi-slant Submanifolds of Locally Metallic Riemannian Manifolds. International Electronic Journal of Geometry 17 2 348–357.
IEEE I. Harry and M. Lone, “Quasi Bi-slant Submanifolds of Locally Metallic Riemannian Manifolds”, Int. Electron. J. Geom., vol. 17, no. 2, pp. 348–357, 2024, doi: 10.36890/iejg.1329607.
ISNAD Harry, Idrees - Lone, Mehraj. “Quasi Bi-Slant Submanifolds of Locally Metallic Riemannian Manifolds”. International Electronic Journal of Geometry 17/2 (September 2024), 348-357. https://doi.org/10.36890/iejg.1329607.
JAMA Harry I, Lone M. Quasi Bi-slant Submanifolds of Locally Metallic Riemannian Manifolds. Int. Electron. J. Geom. 2024;17:348–357.
MLA Harry, Idrees and Mehraj Lone. “Quasi Bi-Slant Submanifolds of Locally Metallic Riemannian Manifolds”. International Electronic Journal of Geometry, vol. 17, no. 2, 2024, pp. 348-57, doi:10.36890/iejg.1329607.
Vancouver Harry I, Lone M. Quasi Bi-slant Submanifolds of Locally Metallic Riemannian Manifolds. Int. Electron. J. Geom. 2024;17(2):348-57.
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