Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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QUASI HEMI-SLANT SUBMANIFOLDS OF KENMOTSU MANIFOLDS

  • PRASAD, RAJENDRA (Department of Mathematics and Astronomy, University of Lucknow) ;
  • HASEEB, ABDUL (Department of Mathematics, College of Science, Jazan University) ;
  • GUPTA, POOJA (Department of Mathematics and Astronomy, University of Lucknow)
  • Received : 2021.06.07
  • Accepted : 2022.01.06
  • Published : 2022.05.30
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Abstract

The main purpose of the present paper is to introduce a brief analysis on some properties of quasi hemi-slant submanifolds of Kenmotsu manifolds. After discussing the introduction and some preliminaries about the Kenmotsu manifold, we worked out some important results in the direction of integrability of the distributions of quasi hemi-slant submanifolds of Kenmotsu manifolds. Afterward, we investigate the conditions for quasi hemi-slant submanifolds of a Kenmotsu manifold to be totally geodesic and later we provide some non-trivial examples to validate the existence of such submanifolds.

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Acknowledgement

The authors are thankful to the editor and anonymous referees for their valuable suggestions towards the improvement of the paper.

References

  1. M.A. Akyol, S. Beyendi, A note on quasi bi-slant submanifolds of cosymplectic manifolds, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 69 (2020), 1508-1521.
  2. A. Ali and C. Ozel, Geometry of warped product pointwise semi-slant submanifolds of cosymplectic manifolds and its applications, Int. J. Geom. Meth. Mod. Phys. 14 (2017), 1750042. https://doi.org/10.1142/S0219887817500426
  3. A. Ali, S. Uddin and W.A.M. Othmam, Geometry of warped product pointwise semi-slant submanifold in Kaehler manifolds, Filomat 31 (2017), 3771-3788. https://doi.org/10.2298/FIL1712771A
  4. A. Carriazo, New developments in slant submanifolds theory, Narosa Publishing House, New Delhi, 2002.
  5. J.L. Cabrerizo, A. Carriazo, L.M. Fernandez, Slant submanifolds in Sasakian manifolds, Glasg. Math. J. 42 (2000), 125-138. https://doi.org/10.1017/s0017089500010156
  6. B.Y. Chen, Geometry of slant submanifolds, Katholieke Universiteit, Leuven, 1990.
  7. B.Y. Chen, Slant immersions, Bull. Austral. Math. Soc. 41 (1990), 135-147. https://doi.org/10.1017/S0004972700017925
  8. S. Dirik and M. Atceken, On the geometry of pseudo-slant submanifolds of cosymplectic manifold, Int. Electron. J. Geom. 9 (2016), 45-56. https://doi.org/10.36890/iejg.591887
  9. S. Dirik and M. Atceken, Contact pseudo-slant submanifolds of a cosymplectic manifold, New Trends in Mathematical Sciences 6 (2018), 154-164. https://doi.org/10.20852/ntmsci.2018.326
  10. 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
  11. A. Haseeb and R. Prasad, Certain curvature conditions in Kenmotsu manifolds with respect to the semi-symmetric metric connection, Commun. Korean Math. Soc. 32 (2017), 1033-1045. https://doi.org/10.4134/CKMS.c160266
  12. S.K. Hui, J. Roy, J. and T. Pal, Warped product pointwise bi-slant submanifolds of kenmotsu manifolds, Asian-European Journal of Mathematics (Online available) https://doi.org/10.1142/S1793557121501692.
  13. J.B. Jun, U.C. De and G. Pathak, On Kenmotsu manifolds, J. Korean Math. Soc. 42 (2005), 435-445. https://doi.org/10.4134/JKMS.2005.42.3.435
  14. K. Kenmotsu, A class of almost contact Riemannian manifolds, Tohoku Math. J. 24 (1972), 93-103. https://doi.org/10.2748/tmj/1178241594
  15. A. Lotta, Slant submanifold in contact geometry, Bull. Math. Soc. Romanie 39 (1996), 183-198.
  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. R. Prasad, S.K. Verma and S. Kumar, Quasi hemi-slant submanifolds of Sasakian manifolds, Journal of Mathematical and Computational Science 10 (2020), 418-435.
  18. N. Papaghiuc, Semi-invariant submanifolds in a Kenmotsu manifolds, Rend. Mat. 3 (1983), 607-622.
  19. N. Papaghiuc, On the geometry of leaves on a semi-invariant ξ⊥-submanifold in a Kenmotsu manifold, An. Stiint. Univ., Al. I. Cuza Iasi 38 (1992), 111-119.
  20. G. Pitis, A remark on Kenmotsu manifolds, Bul. Univ. Brasov Ser. C 30 (1988), 31-32.
  21. R. Prasad, S.K. Verma, S. Kumar and S.K. Chaubey, Quasi hemi-slant submanifolds of Cosymplectic manifolds, Korean J. Math. 28 (2020), 257-273. https://doi.org/10.11568/kjm.2020.28.2.257
  22. R. Prasad, S.S. Shukla, A. Haseeb and S. Kumar, Quasi hemi-slant submanifolds of Kaehler manifolds, Honam Math. J. 42 (2020), 795-809. https://doi.org/10.5831/HMJ.2020.42.4.795
  23. 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
  24. B. Sahin, Slant submanifolds of an almost product Riemannian manifold, J. Korean Math. Soc. 43 (2006), 717-732. https://doi.org/10.4134/JKMS.2006.43.4.717
  25. 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
  26. S.S. Shukla and A. Yadav, Screen Pseudo-Slant Lightlike Submanifolds of Indefinite Sasakian Manifolds, Mediterr. J. Math. 13 (2016), 789-802. https://doi.org/10.1007/s00009-015-0526-2
  27. 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
  28. B. Sahin, Slant submersions from almost Hermitian manifolds, Bull. math. de la Soc. des Sciences Math. de Roumanie 54 (2011), 93-105.
  29. H.M. Tastan, F. Ozdemir, The geometry of hemi-slant submanifolds of a locally product Riemannian manifold, Turk. J. Math. 39 (2015), 268-284. https://doi.org/10.3906/mat-1407-18
  30. S. Tanno, The automorphism groups of almost contact Riemannian manifolds, Tohoku Math. J. 21 (1969), 21-38. https://doi.org/10.2748/tmj/1178243031
  31. S. Uddin, B.Y. Chen and F.R. Al-Solamy, Warped product bi-slant immersions in Kaehler manifolds, Mediterr. J. Math. 14:95 (2017), doi:10.1007/s00009-017-0896-8.