Year 2024,
Volume: 17 Issue: 2, 348 - 357, 27.10.2024
Idrees Harry
,
Mehraj Lone
References
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- [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).
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(2018).
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- [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).
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Mod. Phys. 10(4), Article ID 1320006, 2013.
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- [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.
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(2013).
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- [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).
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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).
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Quasi Bi-slant Submanifolds of Locally Metallic Riemannian Manifolds
Year 2024,
Volume: 17 Issue: 2, 348 - 357, 27.10.2024
Idrees Harry
,
Mehraj Lone
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.
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).