Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
권호 표지
DOI QR코드

DOI QR Code

RIEMANN SOLITONS ON CERTAIN TYPE OF KENMOTSU MANIFOLD

  • Received : 2021.01.20
  • Accepted : 2021.04.06
  • Published : 2021.06.30
Download PDF
⟨ Previous Next ⟩

Abstract

The object of the present paper is to investigate the nature of Riemann solitons on generelized D-conformally deformed Kenmotsu manifold with hyper generalized pseudo symmetric curvature conditions.

Keywords

Acknowledgement

The first named author gratefully acknowledges to UGC, F.No. 16-6(DEC.2018)/2019(NET/CSIR) and UGC-Ref.No. 1147/(CSIR-UGC NET DEC. 2018) for financial assistance.

References

  1. P. Alegre, D. E. Blair, and A. Carriazo, Generalized Sasakian-space-forms, Israel J. Math. 141 (1) (2004), 157-183. https://doi.org/10.1007/BF02772217
  2. K K Baishya, F. Ozen Zengin and J Mike, On hyper generalised weakly symmetric manifolds, Nineteenth International Conference on Geometry, Integrability and Quantization June 02-07, 2017, Varna, Bulgaria Ivailo M. Mladenov and Akira Yoshioka, Editors Avangard Prima, Sofia 2018, pp 1-10 doi:10.7546/giq-19-2018-1-10
  3. K. K. Baishya, P. Peska, and P. R. Chowdhury, On almost generalized weakly symmetric Kenmotsu manifolds, Acta Univ. Palacki. Olomuc., Fac. rer. nat. Mathematica 55 (2) (2016), 5-15.
  4. M. R. Bakshi and K. K. Baishya, Certain types of (LCS)n -manifolds and the case of Riemann solitons, Differential Geometry-Dynamical Systems 22 (2020),11-25.
  5. M. R. Bakshi and K. K. Baishya, Four classes of Riemann solitons on alpa-cosymplectic manifolds, Afrika Matematika, https://doi.org/10.1007/s13370-020-00846-6
  6. M. R. Bakshi, K. K. Baishya, D. G. Prakasha and P. Veeresha, Ricci solitons in a hyper generalized pseudo symmetric D-homothetically deformed Kenmotsu manifold, submitted
  7. A. Biswas, A. Das, K. K. Baishya and M. R. Bakshi, η -Ricci solitons on Kenmotsu manifolds admitting General connection, Korean J. Math. 28 (2020) (4), 803-817, http://dx.doi.org/10.11568/kjm.2020.28.4.803
  8. A. M. Blaga, M. R. Bakshi, and K. K. Baishya, Hyper generalized pseudo Q-symmetric semi-Riemanian manifold, Cubo, A Mathematical Journal,Vol. 23 (1) (2021), 87-96,
  9. K. K. Baishya and P. R. Chowdhury, On Generalized Weakly Symmetric Kenmotsu Manifolds, Bol. Soc. Paran. Mat, (3s.) v. 39 6 (2021): 211-222. https://doi.org/10.5269/bspm.41464
  10. A. M. Blaga, K. K. Baishya and N. Sarkar, Ricci solitons in a generalized weakly (Ricci) symmetric D-homothetically deformed Kenmotsu manifold, Ann. Univ. Paedagog. Crac. Stud. Math. 18 (2019), 123-136 https://doi.org/10.2478/aupcsm-2019-0009
  11. D. E. Blair, Contact Manifolds in Riemannian Geometry, Lect. Notes in Math. 509, Springer-Verlag, New York (1976).
  12. M. C. Chaki, On pseudo symmetric manifolds, Analele Stiintifice ale Universitatii "Al I. Cuza" din Iasi 33 (1987), 53-58.
  13. R. S. Hamilton, The Ricci flow on surfaces , Contemp. Math. 71 (1988), 237-261. https://doi.org/10.1090/conm/071/954419
  14. R. S. Hamilton, Three-manifolds with positive Ricci curvature, J. Diff. Geom. 17 (1982), 255-306.
  15. K. Kenmotsu, A class of almost contact Riemannian manifolds, Tohoku Math. J. 24 (1972), 93-103 https://doi.org/10.2748/tmj/1178241594
  16. Tanno, S., The topology of contact Riemannian manifolds , Illinois J. Math. 12 (1968), 700-717. https://doi.org/10.1215/ijm/1256053971
  17. R. S. Hamilton, The Ricci flow on surfaces, Mathematics and general relativity, Contemp. Math. 71, American Math. Soc. (1988), 237-262.
  18. I.E. Hirica, C. Udriste, Ricci and Riemann solitons , Balkan J. Geom. Applications. 21 (2) (2016), 35-44.
  19. C. Udri,ste, Riemann flow and Riemann wave via bialternate product Riemannian metric. preprint, arXiv.org/math.DG/1112.4279v4 (2012).
  20. C. Udriste, Riemann flow and Riemann wave, Ann. Univ. Vest, Timisoara. Ser. Mat. Inf. 48 (1-2) (2010), 265-274.
  21. Nulifer Ozdemir, Sirin Aktay, Mehmet Solgun, On generalized D-conformal deformations of certain almost contact metric manifolds, Mathematics 2019, 0700168.
  22. Nagaraja, H.G., Kiran Kumar, D.L., Ricci Solitons in Kenmotsu Manifold under Generalized D-Conformal Deformation. Lobachevskii J Math 40 (2019), 195-200. https://doi.org/10.1134/S1995080219020112.
  23. HG Nagaraja, DL Kiran Kumar, VS Prasad, Ricci solitons on Kenmotsu manifolds under D-homothetic deformation, Khayyam J. Math. 4 (1) (2018), 102-109.
  24. T. Suguri and S. Nakayama, D-conformal deformations on almost contact metric structure,Tensor (N.S.) 28 (1974), 125-129.