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WARPED PRODUCT PSEUDO-SLANT SUBMANIFOLDS OF A KENMOTSU MANIFOLD

  • Mohammad Shuaib (Department of Basic Sciences SRMS College of Engineering Technology and Research)
  • Received : 2021.11.30
  • Accepted : 2022.09.21
  • Published : 2023.04.30

Abstract

For a pseudo-slant submanifold of a Kenmotsu manifold, we have worked out conditions in terms its canonical structure tensors, T and F, and its shape operator so that it reduces to a warped product submanifold.

Keywords

References

  1. R. L. Bishop and B. O'Neill, Manifolds of negative curvature, Trans. Amer. Math. Soc. 145 (1969), 1-49. https://doi.org/10.2307/1995057 
  2. J. L. Cabrerizo, A. Carriazo, L. M. Fernandez, and M. Fernandez, Semi-slant submanifolds of a Sasakian manifold, Geom. Dedicata 78 (1999), no. 2, 183-199. https://doi.org/10.1023/A:1005241320631 
  3. J. L. Cabrerizo, A. Carriazo, L. M. Fernandez, and M. Fernandez, Slant submanifolds in Sasakian manifolds, Glasg. Math. J. 42 (2000), no. 1, 125-138. https://doi.org/10.1017/S0017089500010156 
  4. B.-Y. Chen, CR-submanifolds of a Kaehler manifold. I, J. Differential Geometry 16 (1981), no. 2, 305-322. http://projecteuclid.org/euclid.jdg/1214436106  106
  5. B.-Y. Chen, Geometry of slant submanifolds, Katholieke Universiteit Leuven, Louvain, 1990. 
  6. B.-Y. Chen, Geometry of warped product CR-submanifolds in Kaehler manifolds, Monatsh. Math. 133 (2001), no. 3, 177-195. https://doi.org/10.1007/s006050170019 
  7. B.-Y. Chen, Geometry of warped product CR-submanifolds in Kaehler manifolds. II, Monatsh. Math. 134 (2001), no. 2, 103-119. https://doi.org/10.1007/s006050170002 
  8. S. Hiepko, Eine innere Kennzeichnung der verzerrten Produkte, Math. Ann. 241 (1979), no. 3, 209-215. https://doi.org/10.1007/BF01421206 
  9. S. K. Hui, T. Pal, and J. Roy, Another class of warped product skew CR-submanifolds of Kenmotsu manifolds, Filomat 33 (2019), no. 9, 2583-2600.  https://doi.org/10.2298/FIL1909583H
  10. S. K. Hui, J. Roy, and T. Pal, Warped product pointwise bi-slant submanifolds of Kenmotsu manifolds, Asian-Eur. J. Math. 14 (2021), no. 10, Paper No. 2150169, 22 pp. https://doi.org/10.1142/S1793557121501692 
  11. S. K. Hui, M. S. Stankovic, J. Roy, and T. Pal, A class of warped product submanifolds of Kenmotsu manifolds, Turkish J. Math. 44 (2020), no. 3, 760-777. https://doi.org/10.3906/mat-1908-103 
  12. K. Kenmotsu, A class of almost contact Riemannian manifolds, Tohoku Math. J. (2) 24 (1972), 93-103. https://doi.org/10.2748/tmj/1178241594 
  13. V. A. Khan, K. A. Khan, and Siraj-Uddin, CR-warped product submanifolds in a Kaehler manifold, Southeast Asian Bull. Math. 33 (2009), no. 5, 865-874. https://doi.org/10.1016/j.apm.2008.07.014 
  14. V. A. Khan and M. Shuaib, Some warped product submanifolds of a Kenmotsu manifold, Bull. Korean Math. Soc. 51 (2014), no. 3, 863-881. https://doi.org/10.4134/BKMS.2014.51.3.863 
  15. A. Lotta, Slant Submanifolds in contact geometry, Bull. Math. Soc. Romanie 39 (1996), 183-198. 
  16. N. Papaghiuc, Semi-slant submanifolds of a Kaehlerian manifold, An. Stiint. Univ. Al. I. Cuza Iasi Sect. I a Mat. 40 (1994), no. 1, 55-61. 
  17. S. Tanno, The automorphism groups of almost contact Riemannian manifolds, Tohoku Math. J. (2) 21 (1969), 21-38. https://doi.org/10.2748/tmj/1178243031