호남수학학술지 (Honam Mathematical Journal)

  • 제43권4호
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  • Pages.655-665
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  • 2021
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  • 1225-293X(pISSN)
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  • 2288-6176(eISSN)
호남수학회 (The Honam Mathematical Society)
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SOME RESULTS ON INVARIANT SUBMANIFOLDS OF AN ALMOST KENMOTSU (𝜅, 𝜇, 𝜈)-SPACE

  • 투고 : 2021.06.03
  • 심사 : 2021.07.09
  • 발행 : 2021.12.25
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초록

In the present paper, we study the geometric properties of the invariant submanifold of an almost Kenmotsu structure whose Riemannian curvature tensor has (𝜅, 𝜇, 𝜈)-nullity distribution. In this connection, the necessary and sufficient conditions are investigated for an invariant submanifold of an almost Kenmotsu (𝜅, 𝜇, 𝜈)-space to be totally geodesic under the behavior of functions 𝜅, 𝜇, and 𝜈.

키워드

과제정보

We are grateful to all the reviewers for their valuable, detailed and informative suggestions and comments on the drafts of this article.

참고문헌

  1. M. Atceken, U. Yildirim and S. Dirik, Pseudoparallel Invariant Submanifolds of (LCS)n-Manifolds, Korean J. Math. 28(2) (2020), 275-284. https://doi.org/10.11568/kjm.2020.28.2.275
  2. M. Atceken and P. Uygun, Characterizations for Totally Geodesic Submanifolds of (κ, µ)-Paracontact Metric Manifolds, Korean J. Math. 28(3) (2020), 555-571. https://doi.org/10.11568/KJM.2020.28.3.555
  3. A. Bejancu and N. Papaghuic, Semi-Invariant submanifolds of a Sasakain manifold, An. Stiint Univ. Al. I. Cuza. Iai. Sect. I. Mat.(N.S), 27 (1981), 163-170.
  4. D. E. Blair, T. Koufogiorgos and B. J. Papantoniou, Contact metric manifolds satisfying a nullity condition, Israel J. Math. 91 1-3(1995), 189-214. https://doi.org/10.1007/BF02761646
  5. A. Carriazo and V. Martin-Molina, Almost Cosymplectic and Almost Kenmotsu (κ, µ, ν)-Spaces, Mediterr. J. Math.10 (2013), 1551-1571. https://doi.org/10.1007/s00009-013-0246-4
  6. D. Chinea and P.S. Prestelo, Invariant submanifolds of a trans-Sasakian manifold, Publ. Math. Debrecen, 38(1-2) (1991), 103-109.
  7. P. Dacko and Z. Olszak, On Almost Cosympletic (κ, µ, ν)-Spaces, Banach Center Publications, 69(1) (2005), 211-220.
  8. P. Dacko and Z. Olszak, On Almost Cosymplectic (-1, µ, o)-Spaces, Central European Journal of Math. CEJM, (2005), 318-330.
  9. A. De, A Note on the Paper "On Invariant Submanifolds of LP-Sasakian Manifolds", Extracta Math, 28(1) (2013), 33-36.
  10. U. C. De and P. Majhi, On Invariant Submanifolds of Kenmotsu Manifolds, J. Geom, 106 (2015), 109-122. https://doi.org/10.1007/s00022-014-0238-y
  11. Z. Guojing and W. Jiangu, Invariant Submanifolds and Modes of Nonlinear Autonomous Systems, Appl. Math. Mech., 19(7) (1998), 687-693. https://doi.org/10.1007/bf02452377
  12. C. Hu and Y. Wang, A Note Invariant Submanifolds of Trans-Sasakian Manifolds, Int. Electron. J. Geom., 9(2) (2016), 27-35. https://doi.org/10.36890/iejg.584576
  13. T. Koufogiorgos, M. Markellos and V. J. Papantoniou, The Harmonicity of the Reeb Vector Fields on Contact 3-Manifolds Pasific J. Math. 234(2) (2008), 325-344. https://doi.org/10.2140/pjm.2008.234.325
  14. D. Kowalczyk, On Some Subclass of Semisymmetric Manifolds. Soochow J. Math., 27 (2001), 445-461.
  15. G. A. Lobos, M. Ortega, Pseudo-parallel real hypersurfaces in complex space forms, Bull. Korean Math. Soc. 41(4)(2004), 609-618. https://doi.org/10.4134/BKMS.2004.41.4.609
  16. F. Mahi and M. Belkhelfa, On invariant submanifolds of S-manifolds, Bull. Acad. Stiinte Rebup. Mold. Math, 1 (2009), 30-39.
  17. A. Sarkar and M. Sen, On Invariant Submanifolds of LP-Sasakain Manifolds, Extracta Math. 27(1) (2012), 145-154.