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Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2019 / Cilt: 68 - Sayı: 2

On generic submanifold of Sasakian manifold with concurrent vector field

Halil İbrahim YOLDAŞ
Şemsi EKEN MERİÇ
Erol YAŞAR
Pages
1983–1994
Publication Date
2019-08-01
DOI
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AI Summary & Key Takeaways

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

Finally, we give a characterization for a generic submanifold of Sasakian manifold to be a gradient Ricci soliton.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In the present paper, we deal with the generic submanifold admitting a Ricci soliton in Sasakian manifold endowed with concurrent vector field.
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Key Findings & Data:Here, we find that there exists never any concurrent vector field on the invariant distribution D of generic submanifold M.
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Conclusion & Impact:Finally, we give a characterization for a generic submanifold of Sasakian manifold to be a gradient Ricci soliton.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Sasakian manifold · Ricci soliton · concurrent vector field

Abstract

In the present paper, we deal with the generic submanifold admitting a Ricci soliton in Sasakian manifold endowed with concurrent vector field. Here, we find that there exists never any concurrent vector field on the invariant distribution D of generic submanifold M. Also, we provide a necessary and sufficient condition for which the invariant distribution D and anti-invariant distribution D^{⊥} of M are Einstein. Finally, we give a characterization for a generic submanifold of Sasakian manifold to be a gradient Ricci soliton.

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Cite This Article

YOLDAŞ, H. İ., MERİÇ, Ş. E., YAŞAR, E. (2019). On generic submanifold of Sasakian manifold with concurrent vector field. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Cilt: 68 - Sayı: 2, 1983–1994. https://ajindex.com/articles/746981

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References (20)

  1. P. Alegre, Semi-Invariant Submanifolds of Lorentzian Sasakian Manifolds, \emph{Demonstratio Math.} 44:2(2011), 33-38.
  2. M. Atçeken, S. Uddin, Semi-invariant submanifolds of a normal almost paracontact manifold, \emph{Filomat} 31(15) (2017), 4875-4887.
  3. C. S. Bagewadi, G. Ingalahalli, Ricci solitons in Lorentzian $\alpha-$Sasakian manifolds, \emph{Acta Math. Acad. Paedagog. Nyh\'{a}zi. (N.S)} 28(1) (2012), 59-68.
  4. C. L. Bejan, M. Crasmareanu, Second order parallel tensors and Ricci solitons in 3-simensional normal paracontact geometry, \emph{Ann. Glob. Anal. Geom.} 46(2014), 117-127.
  5. A. Bejancu, N. Papaghiuc, Semi-invariant submanifolds of Sasakian manifold, \emph{An. St. Univ. AI. I. Cuza. Iasi} 27(1981), 163-170.
  6. A. Bejancu, N. Papaghiuc, Semi-invariant submanifolds of a Sasakian space form, \emph{Colloq. Math.} 48(1984), 77-88.
  7. A. Bejancu, Geometry of CR-submanifolds, Mathematics and Its Applications (East European Series), (1986).
  8. D. E. Blair, Contact manifolds in Riemannian geometry, Lecture Notes in Mathematics, Springer-Verlag, Berlin, 509(1976).
  9. B.-Y. Chen, S. Deshmukh, Ricci solitons and concurrent vector fields, \emph{Balkan J. Geom. Appl.} 20(1) (2015), 14-25.
  10. B.-Y. Chen, Classification of torqued vector fields and its applications to Ricci solitons, \emph{Kragujevac J. Math.} 41(2) (2017), 239-250.
  11. K. L. Duggal, D. L. Jin, Generic lightlike submanifolds of an indefinite SasakianmManifold, \emph{Int. Electron. J. Geom.} 5(1) (2012), 108-119.
  12. Ghosh, Certain contact metrics as Ricci almost solitons, \emph{Results Maths.} 65(2014), 81-94.
  13. A. Ghosh, Kenmotsu 3-metric as a Ricci soliton, \emph{Chaos, Solitons \& Fractals} 44(8) (2011), 647-650.
  14. R. S. Hamilton, Three-manifolds with positive Ricci curvature, \emph{J. Diff. Geom.} 17(2) (1982), 255-306.
  15. C. He, M. Zhu, The Ricci solitons on Sasakian manifolds, \emph{arxiv:1109.4407v2.} 2011.
  16. G. Ingalahalli, C. S. Bagewadi, Ricci solitons in $\alpha-$Sasakian manifolds, \emph{ISRN Geometry} vol.2012, Article ID 421384, 13 Pages, (2012).
  17. M. A. Khan, M. Z. Khan, Totally umbilical semi-invariant submanifolds of a nearly cosymplectic manifold, \emph{Filomat} 20(2) (2006), 33-38.
  18. M. E. A. Mekki, A. M. Cherif, Generalised Ricci solitons on Sasakian manifolds, \emph{Kyungpook Math. J.} 57(4) (2017), 677-682.
  19. A. Mihai and R. Roşça, On a class of Einstein space-time manifolds, \emph{Publ. Math. Debrecen} 67(2005), 471-480.
  20. H. G. Nagaraja, K. Venu, Ricci solitons in Kenmotsu manifolds, \emph{Journal of Informatic and Ma