Korean Journal of Mathematics

  • 제28권2호
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  • Pages.257-273
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  • 2020
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  • 1976-8605(pISSN)
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  • 2288-1433(eISSN)
강원경기수학회 (The Kangwon-Kyungki Mathematical Society)
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QUASI HEMI-SLANT SUBMANIFOLDS OF COSYMPLECTIC MANIFOLDS

  • Prasad, Rajendra (Department of Mathematics and Astronomy University of Lucknow) ;
  • Verma, Sandeep Kumar (Department of Mathematics and Astronomy University of Lucknow) ;
  • Kumar, Sumeet (Department of Mathematics and Astronomy University of Lucknow) ;
  • Chaubey, Sudhakar K (Section of Mathematics, Department of Information Technology Shinas College of Technology)
  • 투고 : 2019.11.22
  • 심사 : 2020.04.08
  • 발행 : 2020.06.30
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초록

We introduce and study quasi hemi-slant submanifolds of almost contact metric manifolds (especially, cosymplectic manifolds) and validate its existence by providing some non-trivial examples. Necessary and sufficient conditions for integrability of distributions, which are involved in the definition of quasi hemi-slant submanifolds of cosymplectic manifolds, are obtained. Also, we investigate the necessary and sufficient conditions for quasi hemi-slant submanifolds of cosymplectic manifolds to be totally geodesic and study the geometry of foliations determined by the distributions.

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과제정보

The authors express their sincere thanks to the referees and the Editor for providing the valuable suggestions in the improvement of the paper.

참고문헌

  1. A. Ali, and C. Ozel, Geometry of warped product pointwise semi-slant submanifolds of cosymplectic manifolds and its applications, Int. J. Geom. Meth. Mod. Phy. 14 (2017), 1750042. https://doi.org/10.1142/S0219887817500426
  2. A. Ali, S. Uddin and W. A. O. Othmam, Geometry of warped product pointwise semi-slant submanifold in Kaehler manifolds, Filomat 31 (2017), 3771-3788. https://doi.org/10.2298/FIL1712771A
  3. G. Ayar and S. K. Chaubey, M-projective curvature tensor over cosymplectic manifolds, Differential Geometry - Dynamical Systems. 21 (2019), 23-33.
  4. M. Barbero-Linan, et al.: Unified formalison for nonautonomous mechanical systems. J. Math. Phys. 49 ()2008, 062902-062914. https://doi.org/10.1063/1.2929668
  5. A. Benjancu and N. Papaghuic, Semi-invariant Submanifolds of a Sasakian manifold, An. St. Univ. AI. I. Cuza. Iasi. Math. (N.S.) 27 (1981), 163-170.
  6. A. M. Blaga, Invariant, anti-invariant and slant submanifolds of para-Kenmotsu manifold, BSG Publ. 24 (2017), 125-138.
  7. D. E. Blair, Contact manifold in Riemannian geometry, Lecture notes in Math. 509 Springer-Verlag, New-York, (1976).
  8. D. E. Blair and S. I. Goldberg, Topology of almost contact manifolds, J. Differential Geometry 1 (1967), 347-354. https://doi.org/10.4310/jdg/1214428098
  9. J. L. Cabrerizo, A. Carriazo and L. M. Fernandez, Slant submanifolds in Sasakian manifolds, Glasg. Math. J. 42 (2000), 125-138. https://doi.org/10.1017/S0017089500010156
  10. B. Y. Chen, Geometry of slant submanifolds, Katholieke Universiteit, Leuven, (1990).
  11. D. Chinea, M. De-Leon, and J. C. Marrero, Topology of cosymplectic manifolds, J. Math. Pures Appl. (9) 72 (1993), 567-591.
  12. M. De-Leon, E. Merino, J. A. Oubina, P. R. Rodrigues and M. Salgado, Hamiltonian system on K-cosymplectic manifolds, J. Math. Phys. 39(1998), 876-893. https://doi.org/10.1063/1.532358
  13. U. C. De and A. Sarkar, On pseudo-slant submanifolds of trans-Sasakian manifolds, Proc. Esto. Acad. sci. 60 (2011), 1-11. https://doi.org/10.3176/proc.2011.1.01
  14. U. C. De and A. A. Shaikh, Complex manifolds and Contact manifolds, Narosa Publ. House, (2009).
  15. M. Kon, Remarks on anti-invariant submanifolds of a Sasakian manifold, Tensor (N.S.) 30 (1976), 239-245.
  16. J. W. Lee and B. Sahin, Pointwise slant submersions, Bull Korean Math Soc. 51 (2014), 1115-1126. https://doi.org/10.4134/BKMS.2014.51.4.1115
  17. A. Lotta, Slant submanifold in contact geometry, Bull. Math. Soc. Romanie 39 (1996), 183-198.
  18. N. Papaghuic, Semi-slant submanifold of Kaehlerian manifold, An. St. Univ. AI. I. Cuza. Iasi. Math.(N.S.) 9 (1994), 55-61.
  19. K. S. Park and R. Prasad, Semi-slant submersions, Bull. Korean Math. Soc. 50 (2013), 951-962. https://doi.org/10.4134/BKMS.2013.50.3.951
  20. B. Sahin, Warped product submanifolds of a Kaehler manifold with a slant factor, Ann. Pol. Math. 95 (2009), 107-126. https://doi.org/10.4064/ap95-3-2
  21. B. Sahin, Slant submersions from almost Hermitian manifolds, Bull. math. de la Soc. des Sciences Math. de Roumanie 54 (2011), 93-105.
  22. F. Sahin, Cohomology of hemi-slant submanifolds of a Kaehler manifolds, J. Adv. Studies Topology 5 (2014), 27-31. https://doi.org/10.20454/jast.2014.737
  23. M. H. Shahid, et al., Slant submanifolds of cosymplectic manifold, Analele Stiintifice ale Universitatii Al I Cuza din Iasi - Matematica 50 (2004), 33-50.
  24. S. S. Shukla and A. Yadav, Screen Pseudo-Slant Lightlike Submanifolds of Indefinite Sasakian Manifolds, Mediterranean Journal of Mathematics 13 (2016), 789-802. https://doi.org/10.1007/s00009-015-0526-2
  25. S. Uddin, B. Y. Chen and F. R. Al-Solamy, Warped product bi-slant immersions in Kaehler manifolds, Mediterr. J. Math. 14 (2017), 14-95. https://doi.org/10.1007/s00009-016-0837-y
  26. S. K. Yadav and S. K. Chaubey, Certain results on submanifolds of generalized Sasakian-space-forms, Honam Mathematical J. 42 (1) (2020), 123-137. https://doi.org/10.5831/HMJ.2020.42.1.123

피인용 문헌

  1. A note on quasi-bi-slant submanifolds of Sasakian manifolds vol.10, pp.3, 2020, https://doi.org/10.1007/s40065-021-00338-w