Dergiler / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 48 Issue: 2

An inequality for warped product submanifolds of a locally product Riemannian manifold

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Yayın Tarihi
2019-04-01
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

The equality case is also considered.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:Recently, Sahin studied the warped product semi-slant submanifolds of locally product Riemannian manifolds.
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Temel Bulgular & Veri:In this paper, we obtain some geometric properties of such submanifolds with an example.
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Sonuç & Katkı:The equality case is also considered.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:slant submanifolds · semi-slant submanifolds · mixed totally geodesic

Abstract

Recently, Sahin studied the warped product semi-slant submanifolds of locally product Riemannian manifolds. In this paper, we obtain some geometric properties of such submanifolds with an example. Also, we establish a sharp relationship between the squared norm of the second fundamental form and the warping function in terms of the slant angle. The equality case is also considered.

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Bu Makaleye Atıf Yap

Al-solamy, F. R., Uddin, S. (2019). An inequality for warped product submanifolds of a locally product Riemannian manifold. Hacettepe Journal of Mathematics and Statistics, Volume: 48 Issue: 2. https://ajindex.com/articles/1402803

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Kaynakça (18)

  1. M. Atceken, Warped product semi-slant submanifolds in locally Riemannian product manifolds, Bull. Austral. Math. Soc. 77, 177–186, 2008.
  2. M. Atceken, Geometry of warped product semi-invariant submanifolds of a locally Riemannian product manifold, Serdica Math. J. 35, 273–286, 2009.
  3. M. Atceken, Warped product semi-invariant submanifolds in locally decomposable Riemannian manifolds, Hacet. J. Math. Stat. 40, 401–407, 2011.
  4. A. Bejancu, Semi-invariant submanifolds of locally Riemannian product manifolds, Ann. Univ. Timisoara S. Math. 22, 3–11, 1984.
  5. R.L. Bishop and B. O’Neill, Manifolds of Negative curvature, Trans. Amer. Math. Soc. 145, 1–49, 1969.
  6. B.Y. Chen, Slant immersions, Bull. Austral. Math. Soc. 41, 135–147, 1990.
  7. H. Li and X. Li, Semi-slant submanifolds of locally product manifolds, Georgian Math. J. 12, 273–282, 2005.
  8. K. Matsumoto, On submanifolds of locally product Riemannian manifolds, TRU Math. 18, 145–157, 1982.
  9. N. Papaghiuc, Semi-slant submanifolds of Kaehlerian manifold, Ann. St. Univ. Iasi, 9, 55–61, 1994.
  10. B. Sahin, Slant submanifolds of an almost product Riemannian manifold, J. Korean Math. Soc. 43, 717–732, 2006.
  11. B. Sahin, Warped product semi-invariant submanifolds of locally product Riemannian manifolds, Bull. Math. Soc. Sci. Math. Roumanie Tome, 49 (97), 383–394, 2006.
  12. B. Sahin, Warped product semi-slant submanifolds of a locally product Riemannian manifold, Studia Sci. Math. Hungar. 46, 169–184, 2009.
  13. S. Uddin and F.R. Al-Solamy, Warped product pseudo-slant submanifolds of cosymplectic manifolds, An. Ştiinţ. Univ. Al. I. Cuza Iaşi Mat. (N.S.) Tomul LXII, (f. 2,3), 901–913, 2016.
  14. S. Uddin and F.R. Al-Solamy, Warped product pseudo-slant immersions in Sasakian manifolds, Publ. Math. Debrecen, 91 (3-4), 331–348, 2017.
  15. S. Uddin, A. Ali, N.M. Al-Asmari and W.A. Othman, Warped product pseudo-slant submanifolds in a locally product Riemannian manifold, Diff. Geometry Dyn. Syst. 18, 147–158, 2016.
  16. S. Uddin, B.Y. Chen and F.R. Al-Solamy, Warped product bi-slant im- mersions in Kaehler manifolds, Mediterr. J. Math. 14, Art. 95, 1–11, 2017.
  17. S. Uddin and A.Y.M. Chi, Warped product pseudo-slant submanifolds of nearly Kaehler manifolds, An. St. Univ. Ovidius Constanta, 19 (3), 195–204, 2011.
  18. K. Yano and M. Kon, Structures on manifolds, Series in Pure Mathematics, World Scientific Publishing Co., Singapore, 1984.