SavedAdd your journal

Journals / International Electronic Journal of Geometry / 2024 / Volume: 17 Issue: 2

Metallic Structures on Product Manifolds and Chen-Ricci Inequalities

Mustafa Gök(MİLLİ SAVUNMA ÜNİVERSİTESİ)0000-0001-6346-0758
Pages
—
Publication Date
2024-10-27
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Moreover, the equality cases are considered in order to characterize these submanifolds.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, we discuss metallic structures on product manifolds and derive the Chen-Ricci inequalities for remarkable submanifolds determined by the behaviour of their tangent bundles with regard to the action of the metallic structure in a locally decomposable metallic Riemannian manifold whose components are spaces of constant curvature.
📊
Key Findings & Data:In this study, we discuss metallic structures on product manifolds and derive the Chen-Ricci inequalities for remarkable submanifolds determined by the behaviour of their tangent bundles with regard to the action of the metallic structure in a locally decomposable metallic Riemannian manifold whose components are spaces of constant curvature.
💡
Conclusion & Impact:Moreover, the equality cases are considered in order to characterize these submanifolds.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Metallic structure · metallic Riemannian manifold · Riemannian submanifold

Abstract

In this study, we discuss metallic structures on product manifolds and derive the Chen-Ricci inequalities for remarkable submanifolds determined by the behaviour of their tangent bundles with regard to the action of the metallic structure in a locally decomposable metallic Riemannian manifold whose components are spaces of constant curvature. Moreover, the equality cases are considered in order to characterize these submanifolds.

🔖

Cite This Article

Gök, M. (2024). Metallic Structures on Product Manifolds and Chen-Ricci Inequalities. International Electronic Journal of Geometry, Volume: 17 Issue: 2. https://doi.org/10.36890/iejg.1458491

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (38)

  1. Bejancu, A.: Geometry of CR Submanifolds. D. Reidel Publishing Company, Dordrecht (1986).
  2. Blaga, A. M.: The geometry of golden conjugate connections. Sarajevo J. Math. 10 (23), 237-245 (2014).
  3. 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).
  4. Blaga, A. M., Hretcanu, C. E.: Metallic conjugate connections. Rev. Un. Mat. Argentina 59 (1), 179-192 (2018).
  5. Blaga, A. M., Hretcanu, C. E.: Remarks on metallic warped product manifolds. Facta Univ. Ser. Math. Inform. 33 (1), 269-277 (2018).
  6. Chen, B. Y.: Mean curvature and shape operator of isometric immersions in real space forms. Glasgow. Math. J. 38 (1), 87-97 (1996).
  7. Chen, B. Y.: Relations between Ricci curvature and shape operator for submanifolds with arbitrary codimension. Glasgow Math. J. 41 (1), 33-41 (1999).
  8. Choudhary, M. A., Blaga, A. M.: Inequalities for generalized normalized δ-Casorati curvatures of slant submanifolds in metallic Riemannian space forms. J. Geom. 111 (3), Article ID 39, 18 pages (2020).
  9. Crâşmareanu, M. C., Hretcanu, C. E.: Golden differential geometry. Chaos Soliton. Fract. 38 (5), 1229-1238 (2008).
  10. de Spinadel, V. W.: The family of metallic means. Vis. Math. 1 (3), (1999).
  11. de Spinadel, V. W.: The metallic means family and multifractal spectra. Nonlinear Anal. 36 (6), 721-745 (1999).
  12. de Spinadel, V. W.: The metallic means family and renormalization group techniques. Proc. Steklov Inst. Math. (suppl. 1), 194-209 (2000).
  13. de Spinadel, V. W.: The metallic means family and forbidden symmetries. Int. Math. J. 2 (3), 279-288 (2002).
  14. Eken, Ş., Gülbahar, M., Kılıç, E.: Some inequalities for Riemannian submersions. An. ¸Stiin¸t. Univ. Al. I. Cuza Ia¸si. Mat. (N.S.) 63 (3), 471-482 (2017).
  15. Etayo, F., Santamaría, R., Upadhyay, A.: On the geometry of almost golden Riemannian manifolds. Mediterr. J. Math. 14 (5), Article ID 187, 14 pages (2017).
  16. Gezer, A., Karaman, Ç.: On metallic Riemannian structures. Turk. J. Math. 3 (6), 954-962 (2015).
  17. Gök, M., Keleş, S., Kılıç, E.: Schouten and Vranceanu connections on golden manifolds. Int. Electron. J. Geom. 12 (2), 169-181 (2019).
  18. Gök, M., Keleş, S., Kılıç, E.: Some characterizations of semi-invariant submanifolds of golden Riemannian manifolds. Mathematics 7 (12), Article ID 1209, 12 pages (2019).
  19. Gülbahar, M., Eken, Ş., Kılıç, E.: Sharp inequalities involving the Ricci curvature for Riemannian submersions. Kragujevac J. Math. 41 (2), 279-293 (2017).
  20. Hong, S., Matsumoto, K., Tripathi, M. M.: Certain basic inequalities for submanifolds of locally conformal Kahler space forms. SUT J. Math. 41 (1), 75-94 (2005).
  21. Hong, S., Tripathi, M. M.: On Ricci curvature of submanifolds. Int. J. Pure Appl. Math. Sci. 2 (2), 227-245 (2005).
  22. Hretcanu, C. E., Blaga, A. M.: Submanifolds in metallic Riemannian manifolds. Differ. Geom. Dyn. Syst. 20, 83-97 (2018).
  23. Hretcanu, C. E., Blaga, A. M.: Slant and semi-slant submanifolds in metallic Riemannian manifolds. J. Funct. Spaces 2018 (3), Article ID 2864263, 13 pages (2018).
  24. Hretcanu, C. E., Blaga, A. M.: Hemi-slant submanifolds in metallic Riemannian manifolds. Carpathian J. Math. 35 (1), 59-68 (2019).
  25. Hretcanu, C. E., Crâşmareanu, M. C.: On some invariant submanifolds in a Riemannian manifold with golden structure. An. Ştiint. Univ. Al. I. Cuza Iaşi. Mat. (N.S.) 53 (suppl. 1), 199-211 (2007).
  26. Hretcanu, C. E., Crâşmareanu, M. C.: Applications of the golden ratio on Riemannian manifolds. Turk. J. Math. 33 (2), 179-191 (2009).
  27. Hretcanu, C. E., Crâşmareanu, M. C.: Metallic structures on Riemannian manifolds. Rev. Un. Mat. Argentina 54 (2), 15-27 (2013).
  28. Kılıç, E., Tripathi, M. M., Gülbahar, M.: Chen-Ricci inequalities for submanifolds of Riemannian and Kaehlerian product manifolds. Ann. Pol. Math. 116 (1), 37-56 (2016).
  29. Kim, J. S., Tripathi, M. M., Choi, J.: Ricci curvature of submanifolds in locally conformal almost cosyplectic manifolds. Indian J. Pure Appl. Math. 35 (3), 259-271 (2004).
  30. Mihai, A.: Inequalities on the Ricci curvature. J. Math. Inequal. 9 (3), 811-822 (2015).
  31. Mihai, I.: Ricci curvature of submanifolds in Sasakian space forms. J. Aust. Math. Soc. 72 (2), 247-256 (2002).
  32. Mustafa, A., Uddin, S., Al-Solamy, F. R.: Chen-Ricci inequality for warped products in Kenmotsu space forms and its applications. RACSAM 113 (4), 3585-3602 (2019).
  33. Özgür, C., Özgür, N. Y.: Classification of metallic shaped hypersurfaces in real space forms. Turk. J. Math. 39 (5), 784-794 (2015).
  34. Özgür, C., Özgür, N. Y.: Metallic shaped hypersurfaces in Lorentzian space forms. Rev. Un. Mat. Argentina 58 (2), 215-226 (2017).
  35. Tripathi, M. M.: Chen-Ricci inequality for submanifolds of contact metric manifolds. J. Adv. Math. Stud. 1 (1-2), 111-134 (2008).
  36. Vîlcu, G. E.: B.-Y. Chen inequalities for slant submanifolds in quaternionic space forms. Turk. J. Math. 34 (1), 115-128 (2010).
  37. Yano, K., Kon, M.: Structures on Manifolds. World Scientific, Singapore (1984).
  38. Yoon, D. W.: Inequality for Ricci curvature of slant submanifolds in cosymplectic space forms. Turk. J. Math. 30 (1), 43-56 (2006)