A Study on \(W_6\) and \(W_8\)-Curvature Tensors on \((LPK)_n\)-Manifold with a Quarter-Symmetric Metric Connection

Prasad, Rajendra; Haseeb, Abdul; Sen, Sushmita; Bilal, Mohd

doi:10.28924/2291-8639-23-2025-114

Research Article

A Study on \(W_6\) and \(W_8\)-Curvature Tensors on \((LPK)_n\)-Manifold with a Quarter-Symmetric Metric Connection

Rajendra Prasad
Abdul Haseeb*
Sushmita Sen
Mohd Bilal

* Corresponding author

Abstract

The present paper deals with the study of W₆ and W₈-curvature tensors in an n-dimensional Lorentzian para-Kenmotsu manifold (briefly, (LPK)_n-manifold) with a quarter-symmetric metric connection.

How to Cite

R. Prasad, A. Haseeb, S. Sen, M. Bilal, A Study on \(W_6\) and \(W_8\)-Curvature Tensors on \((LPK)_n\)-Manifold with a Quarter-Symmetric Metric Connection, Int. J. Anal. Appl. 23 (2025), 114. https://doi.org/10.28924/2291-8639-23-2025-114

BibTeX

@article{Prasad2025,
  author  = {Prasad, Rajendra and Haseeb, Abdul and Sen, Sushmita and Bilal, Mohd},
  title   = {A Study on \(W_6\) and \(W_8\)-Curvature Tensors on \((LPK)_n\)-Manifold with a Quarter-Symmetric Metric Connection},
  journal = {Int. J. Anal. Appl.},
  volume  = {23},
  year    = {2025},
  pages   = {114},
  doi     = {10.28924/2291-8639-23-2025-114}
}

References

[1] K. Kenmotsu, A Class of Almost Contact Riemannian Manifolds, Tohoku Math. J. 24 (1972), 93–103. https://doi.org/10.2748/tmj/1178241594.
[2] H.I. Yolda¸s, E. Yasar, Some Notes on Kenmotsu Manifold, Facta Univ., Ser. Math. Inform. (2021), 949–961. https://doi.org/10.22190/FUMI2004949Y.
[3] J.B. Jun, U.C. De, G. Pathak, On Kenmotsu Manifolds, J. Korean Math. Soc. 42 (2005), 435–445. https://doi.org/10.4134/JKMS.2005.42.3.435.
[4] R. Prasad, A. Haseeb, P. Gupta, Quasi Hemi-Slant Submanifolds of Kenmotsu Manifolds, J. Appl. Math. Inform. 40 (2022), 475–490. https://doi.org/10.14317/JAMI.2022.475.
[5] I. Sato, On a Structure Similar to the Almost Contact Structure I, Tensor, N. S. 30 (1976), 219–224. https://cir.nii.ac.jp/crid/1572261550129279744.
[6] S. Kaneyuki, M. Kozai, Paracomplex Structures and Affine Symmetric Spaces, Tokyo J. Math. 8 (1985), 81–98. https://doi.org/10.3836/tjm/1270151571.
[7] S. Kaneyuki, F.L. Williams, Almost Paracontact and Parahodge Structures on Manifolds, Nagoya Math. J. 99 (1985), 173–187. https://doi.org/10.1017/S0027763000021565.
[8] B.B. Sinha, K.L.S. Prasad, A Class of Almost Para Contact Metric Manifolds, Bull. Calcutta Math. Soc. 87 (1995), 307–312.
[9] B. O’Neill, Semi-Riemannian Geometry: With Applications to Relativity, Academic Press, New York, 1983.
[10] V.R. Kaigorodov, The Curvature Structure of Spacetime, Prob. Geom. 14 (1983), 177–202.
[11] A.K. Raychaudhuri, S. Banerji, A. Banerjee, General Relativity, Astrophysics and Cosmology, Springer, 1992.
[12] A. Haseeb, R. Prasad, Certain Results on Lorentzian Para-Kenmotsu Manifolds, Bol. Soc. Parana. Mat. 39 (2021), 201–220. https://doi.org/10.5269/bspm.40607.
[13] A. Haseeb, R. Prasad, Some Results on Lorentzian Para-Kenmotsu Manifolds, Bull. Transilv. Univ. Bras, ov Ser. III Math. Inform. Phys. 13 (2020), 185–198. https://doi.org/10.31926/but.mif.2020.13.62.1.14.
[14] S. Golab, On Semi-Symmetric and Quarter-Symmetric Linear Connections, Tensor, N. S. 29 (1975), 249–254.
[15] K. Mandal, U.C. De, Quarter-Symmetric Metric Connection in a P-Sasakian Manifold, Ann. West Univ. Timisoara - Math. Comput. Sci. 53 (2015), 137–150. https://doi.org/10.1515/awutm-2015-0007.
[16] M. Ahmad, J.B. Jun, A. Haseeb, Hypersurfaces of Almost-Para Contact Riemannian Manifold With a QuarterSymmetric Connection, Bull. Korean Math. Soc. 46 (2009), 477–487. https://doi.org/10.4134/BKMS.2009.46.3.477.
[17] R. Prasad, A. Haseeb, Conformal Curvature Tensor on K-Contact Manifolds With Respect to the Quarter-Symmetric Metric Connection, Facta Univ. (NIS) Ser. Math. Inform. 32 (2017), 503–514.
[18] G.P. Pokhariyal, Relativistic Significance of Curvature Tensors, Int. J. Math. Math. Sci. 5 (1982), 133–139.
[19] R. Prasad, A. Haseeb, V.S. Yadav, A Study of ϕ-Ricci Symmetric LP-Kenmotsu Manifolds, Int. J. Maps Math. 7 (2024), 33–44.
[20] P.W. Njori, N.K. Moindi, G.P. Pokhariyal, A Study on W6-Curvature Tensors and W8-Curvature Tensors in Kenmotsu Manifold Admitting Semi-Symmetric Metric Connection, Int. J. Stat. Appl. Math. 6 (2021), 1–5.
[21] G.P. Pokhariyal, R.S. Mishra, Curvature Tensors and Their Relativistics Significance, Yokohama Math. J. 18 (1970), 105–108.