International Journal of Mathematics Trends and Technology
Volume 68 | Issue 11 | Year 2022 | Article Id. IJMTT-V68I11P507 | DOI : https://doi.org/10.14445/22315373/IJMTT-V68I11P507
| Received | Revised | Accepted | Published |
|---|---|---|---|
| 05 Oct 2022 | 09 Nov 2022 | 19 Nov 2022 | 30 Nov 2022 |
In this paper, we study the notions of W4-flat para-Kenmotsu, semi-symmetric para-Kenmotsu and symmetric and recurrent relationships with respect to the W4-curvature tensor.
[1] T. Adati and K. Matsumoto, “On Conformally Recurrent and Conformally Symmetric P_Sasakian Manifolds”, TRU Math, vol. 13, pp. 25-32, 1977.
[2] T. Adati and T. Miyazawa, “On Paracontact Riemannian Manifolds,” TRU Math, vol. 13, no. 2, pp. 27-39, 1977.
[3] K. De and U. C. De, “Conharmonic Curvature Tensor on Kenmotsu Manifolds,” Bulletin of the Transilvania University of Bra¸sov , vol. 6(55), no. 1, pp. 9-22, 2013.
[4] U. C. De and N. Guha, “On Conharmonic Recurrent Sasakian Manifold,” Indian Journal Mathematics, vol. 34, pp. 209-215, 1992.
[5] K. Kenmotsu, “A Class of Almost Riemannian Manifolds,” Tohoku Mathematical Journal, vol. 24, no. 1, pp. 25-32, 1972. Crossref, https://doi.org/10.2748/tmj/1178241594
[6] Jaeman Kim, “On W4-Birecurrent Manifolds,” Honam Mathematical Journal, vol. 36 no. 4, pp. 723-730 , 2014. Crossref, https://doi.org/10.5831/HMJ.2014.36.4.723
[7] Jaeman Kim, “On Pseudo W4-Symmetric Manifolds,” Honam Mathematical Journal, vol. 38, no. 1, pp. 34-45, 2016. Crossref, https://doi.org/10.5831/HMJ.2016.38.1.39
[8] D. T. Leyson and R. S. Lemence, “On W4-Flatness of Some Classes of Generalizations of Einstein Manifolds,” International Journal of Mathematical Analysis, vol. 8 no. 18, pp. 1881-889, 2014. ---the paper is not in that journal
[9] Abhijit Mandal, and Ashis Biswas, “Some Curvature Properties of Para-Kenmotsu Manifolds with Respect to Zamkovoy Connection,” Journal of Hyperstructures, vol. 11, no. 1, pp. 166-182, 2022.
[10] M. Manev and M. Staikova, “On Almost Paracontact Riemannian Manifolds of Type (n,n)," Journal of Geometry, vol. 72, no. 1, pp. 108-114, 2001. Crossref, https://doi.org/10.1007/s00022-001-8572-2
[11] Neelam Pandey, Mayank Pandey, and R. N. Singh, “Space-Time Admitting W4-Curvature Tensor,” Journal of International Academy of Physical Sciences, vol. 25, no. 1, pp. 25-35, 2021.
[12] Pokhariyal, G. P., Mishra, R. S., “Curvature Tensors and Their Relativistic Significance III,” The Yokohama Mathematical journal, vol. 20, pp. 105-108, 1973.
[13] G. P. Pokhariyal, “Curvature Tensors In Riemannian Manifold II,” Proceedings of the Indian Academy of Sciences - Section A, vol. 79, pp. 105-110, 1974. Crossref, https://doi.org/10.1007/BF03046662
[14] G. P. Pokhariyal, “On Symmetric Sasakian Manifold,” Kenya Journal Science Series A , vol. (1-2), pp. 39-42, 1988.
[15] G. P. Pokhariyal, “Curvature Tensors in a Lorentzian Para-Sasakian Manifold,” Quaestiones Math, vol. 19, no. 12 , pp. 129-136, 1996.
[16] G. P. Pokhariyal and R. S. Mishra, “Curvature Tensors and Their Relativistic Significance II,” Yokohama Mathematical Journal, vol. 19, no. 2, pp. 97-103, 1971.
[17] K. L. Sai Prasad, S. Sunitha Devi, and G. V. S. R. Deekshitulu, “On a Class of P-Kenmotsu Manifolds Admitting Weyl-Projective Curvature Tensor of Type (1,3),” Turkish Journal of Analysis and Number Theory, vol. 6, no. 6, pp. 155-158, 2018. Crossref, https://doi.org/0.12691/tjant-6-6-2
[18] S. Sasaki, “On Paracontact Riemannian Manifolds,” TRU Math, vol. 16-2, pp. 75-86, 1980.
[19] T. Sato, “On Structure Similar to the Almost-Contact Structure,” Tensor (N.S), vol. 30, pp. 219-224, 1976.
[20] T. Satyanarayana and K. L. Sai Prasad, “On a Type of Para-Kenmotsu Manifold,” Pure Mathematical Sciences, vol. 2, no. 4, pp. 165- 170, 2013.
[21] T. Satyanarayana and K. L. Sai Prasad, “On Semi-Symmetric Para-Kenmotsu Manifolds,” Turkish Journal of Analysis and Number Theory, vol. 3, no. 6, pp. 145-148, 2015. Crossref, https://doi.org/10.12691/tjant-3-6-1
[22] B. B. Sinha and K. L. Sai Prasad, “A Class of Almost Contact Metric Manifolds,” Bulletin of the Calculatta Mathematical Society, vol. 87, pp. 307-312, 1995.
[23] B. B. Sinha and K. L. Sai Prasad, “A Class of Almost Para-Contact Metric Manifolds,” Bulletin of the Calculatta Mathematical Society Society, vol. 87, pp. 307-312, 1995.
[24] Z. I. Szabo, “Structure Theorems on Riemannian Spaces Satisfying R(X,Y) R=0." Geometriae Dedicata, vol. 19, pp. 65-108, 1985. Crossref, https://doi.org/10.1007/BF00233102
25] Simeon Zamkovoy, “On Para-Kenmotsu Manifolds,” Filomat, vol. 32, no. 14, pp. 4971-4980, 2018.
Stephen K. Moindi, Bernard M. Nzimbi, "Study of W4-Curvature Tensor in Para-Kenmotsu Manifolds," International Journal of Mathematics Trends and Technology (IJMTT), vol. 68, no. 11, pp. 73-78, 2022. Crossref, https://doi.org/10.14445/22315373/IJMTT-V68I11P507
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