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Dergiler / International Electronic Journal of Geometry / 2026 / Volume: 16 Issue: 1

The Stability Problem of Certain Anti-Invariant Submanifolds in Golden Riemannian Manifolds

Mustafa Gök(Sivas Cumhuriyet University)0000-0001-6346-0758
Erol Kılıç(INONU UNIVERSITY)0000-0001-7536-0404
Sayfa
—
Yayın Tarihi
2023-04-30
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

In this study, we discuss the stability of some anti-invariant submanifolds of golden Riemannian manifolds under certain conditions in terms of the Ricci curvature tensors of the ambient manifold and the submanifold.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this study, we discuss the stability of some anti-invariant submanifolds of golden Riemannian manifolds under certain conditions in terms of the Ricci curvature tensors of the ambient manifold and the submanifold.
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Temel Bulgular & Veri:In this study, we discuss the stability of some anti-invariant submanifolds of golden Riemannian manifolds under certain conditions in terms of the Ricci curvature tensors of the ambient manifold and the submanifold.
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Sonuç & Katkı:In this study, we discuss the stability of some anti-invariant submanifolds of golden Riemannian manifolds under certain conditions in terms of the Ricci curvature tensors of the ambient manifold and the submanifold.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Stability · metallic Riemannian manifold · anti-invariant submanifold

Abstract

In this study, we discuss the stability of some anti-invariant submanifolds of golden Riemannian manifolds under certain conditions in terms of the Ricci curvature tensors of the ambient manifold and the submanifold.

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Bu Makaleye Atıf Yap

Gök, M., Kılıç, E. (2023). The Stability Problem of Certain Anti-Invariant Submanifolds in Golden Riemannian Manifolds. International Electronic Journal of Geometry, Volume: 16 Issue: 1. https://doi.org/10.36890/iejg.1240437

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Kaynakça (31)

  1. Bahadır, O., Uddin, S.: Slant submanifolds of golden Riemannian manifolds. J. Math. Ext. 13(4), 23-39 (2019).
  2. Bejancu, A.: Geometry of CR Submanifolds. D. Reidel Publishing Company. Dordrecht (1986).
  3. Blaga, A.M.: The geometry of golden conjugate connections. Sarajevo J. Math. 10(23), 237-245 (2014).
  4. Blaga, A.M., Hreţcanu, C.E.: Golden warped product Riemannian manifolds. Libertas Math. 37(1), 1-11 (2017).
  5. Blaga, A.M., Hreţcanu, C.E.: Invariant, anti-invariant and slant submanifolds of a metallic Riemannian manifold. Novi Sad J. Math. 48(2), 55-80 (2018).
  6. Cîrnu, M.: Stability of slant and semi-slant submanifolds in Sasaki manifolds. Acta Univ. Apulensis 20, 63-78 (2009).
  7. Chen, B.Y., Morvan, J.M.: Deformations of isotropic submanifolds in Kahler manifolds. J. Geom. Phys. 13(1), 79-104 (1994).
  8. Chen, B.Y., Leung, P.F., Nagano, T.: Totally geodesic submanifolds of symmetric spaces, III. Preprint, (1980).
  9. Crâşmăreanu, M.C., Bercu, G.: Semi-invariant submanifolds in metric geometry of endomorphisms. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 90(1), 87–92 (2020).
  10. Crâşmăreanu, M.C., Hreţcanu, C.E.: Golden differential geometry. Chaos Solitons Fractals 38(5), 1229-1238 (2008).
  11. Crâşmăreanu, M.C., Hreţcanu, 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, 9 pages (2013).
  12. Erdoğan, F.E., Yıldırım, C.: On a study of the totally umbilical semi-invariant submanifolds of golden Riemannian manifolds. J. Polytechnic 21(4), 967-970 (2018).
  13. Goldberg, S.I., Yano, K.: Polynomial structures on manifolds. Kodai Math. Sem. Rep. 22(2), 199-218 (1970).
  14. 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).
  15. Gök, M., Keleş, S., Kılıç, E.: Invariant submanifolds in golden Riemannian manifolds. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 69(2), 125-138 (2020).
  16. Gök, M., Kılıç, E., Keleş, S.: Anti-invariant submanifolds of locally decomposable golden Riemannian manifolds. Balk. J. Geom. Appl. 25(1), 47-60 (2020).
  17. Hreţcanu, C.E., Blaga, A.M.: Submanifolds in metallic Riemannian manifolds. Differ. Geom. Dyn. Syst. 20, 83-97 (2018).
  18. Hreţcanu, C.E., Blaga, A.M.: Slant and semi-slant submanifolds in metallic Riemannian manifolds. J. Funct. Spaces 2018, Article ID 2864263, 13 pages (2018).
  19. Hreţcanu, C.E., Blaga, A.M.: Hemi-slant submanifolds in metallic Riemannian manifolds. Carpathian J. Math. 35(1), 59-68 (2019).
  20. Hreţcanu, C.E., Crâşmăreanu, M.C.: On some invariant submanifolds in a Riemannian manifold with golden structure. An. Ştiinţ. Univ. Al. I. Cuza Ia¸si. Mat. (N.S.) 53(suppl. 1), 199-211 (2007).
  21. Hreţcanu, C.E., Crâşmăreanu, M.C.: Applications of the golden ratio on Riemannian manifolds. Turk. J. Math. 33(2), 179-191 (2009).
  22. Hreţcanu, C.E., Crâşmăreanu, M.C.: Metallic structures on Riemannian manifolds. Rev. Un. Mat. Argentina 54(2), 15-27 (2013).
  23. Lawson, H.B.: Minimal Varieties in Real and Complex Geometry. Presses de l’Université de Montréal, Montreal (1974).
  24. Oh, Y.G.: Second variation and stability of minimal Lagrangian submanifolds. Invent. Math. 101(2), 501-519 (1990).
  25. Özgür, C., Özgür, N.Y.: Classification of metallic shaped hypersurfaces in real space forms. Turk. J. Math. 39(5), 784-794 (2015).
  26. Özgür, C., Özgür, N.Y.: Metallic shaped hypersurfaces in Lorentzian space forms. Rev. Un. Mat. Argentina 58(2), 215-226 (2017).
  27. Özkan, M.: Prolongations of golden structures to tangent bundles. Differ. Geom. Dyn. Syst. 16, 227-238 (2014).
  28. Pitiş, G.: On some submanifolds of a locally product manifold. Kodai Math. J. 9(3), 327-333 (1986).
  29. Renteln, P.: Manifolds, Tensors, and Forms. Cambridge University Press. New York (2014).
  30. Yano, K.: Integral Formulas in Riemannian Geometry. Marcel Dekker. Newyork (1970).
  31. Yano, K., Kon, M.: Structures on Manifolds. World Scientific. Singapore (1984).