Araştırma Makalesi
BibTex RIS Kaynak Göster

Yıl 2024, Cilt: 17 Sayı: 2, 348 - 357

Idrees Harry , Mehraj Lone

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

Öz

Kaynakça

  • [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

Yıl 2024, Cilt: 17 Sayı: 2, 348 - 357

Idrees Harry , Mehraj Lone

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

Öz

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.

Anahtar Kelimeler

Metallic Riemannian manifolds quasi bi-slant submanifolds distribution

Kaynakça

  • [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).
Toplam 25 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Cebirsel ve Diferansiyel Geometri
Bölüm Araştırma Makalesi
Yazarlar

Idrees Harry 0000-0003-3930-2009

Mehraj Lone 0000-0002-4764-9224

Erken Görünüm Tarihi 16 Eylül 2024
Yayımlanma Tarihi
Kabul Tarihi 9 Kasım 2023
Yayımlandığı Sayı Yıl 2024 Cilt: 17 Sayı: 2

Kaynak Göster

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. Eylül 2024;17(2):348-357. doi:10.36890/iejg.1329607
Chicago Harry, Idrees, ve Mehraj Lone. “Quasi Bi-Slant Submanifolds of Locally Metallic Riemannian Manifolds”. International Electronic Journal of Geometry 17, sy. 2 (Eylül 2024): 348-57. https://doi.org/10.36890/iejg.1329607.
EndNote Harry I, Lone M (01 Eylül 2024) Quasi Bi-slant Submanifolds of Locally Metallic Riemannian Manifolds. International Electronic Journal of Geometry 17 2 348–357.
IEEE I. Harry ve M. Lone, “Quasi Bi-slant Submanifolds of Locally Metallic Riemannian Manifolds”, Int. Electron. J. Geom., c. 17, sy. 2, ss. 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 (Eylül 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 ve Mehraj Lone. “Quasi Bi-Slant Submanifolds of Locally Metallic Riemannian Manifolds”. International Electronic Journal of Geometry, c. 17, sy. 2, 2024, ss. 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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