Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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CERTAIN RESULTS ON THREE-DIMENSIONAL f-KENMOTSU MANIFOLDS WITH CONFORMAL RICCI SOLITONS

  • Received : 2020.12.11
  • Accepted : 2021.12.29
  • Published : 2022.03.30
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Abstract

In the present paper, we have studied conformal Ricci solitons on f-Kenmotsu manifolds of dimension three. Also we have studied 𝜙-Ricci symmetry, 𝜂-parallel Ricci tensor, cyclic parallel Ricci tensor and second order parallel tensor in f-Kenmotsu manifolds of dimension three admitting conformal Ricci solitons. Finally, we give an example.

Keywords

Acknowledgement

The author is thankful to the referee for his/her valuable suggestions towards the improvement of the paper.

References

  1. D.E. Blair, Contact Manifolds in Riemannian Geometry, Lecture Notes in Math., 509 (1976), Springer-Verlag.
  2. N. Basu and A. Bhattacharyya, Conformal Ricci soliton in Kenmotsu manifold, Global J. of Adv. Res. on classical and modern Geom. 4 (1) (2015), 15-21.
  3. C. L. Bejan and M. Crasmareanu, Ricci solitons in manifolds with quasi-constant curvature, Publ. Math. Debrecen 78 (1) (2011), 235-243. https://doi.org/10.5486/PMD.2011.4797
  4. S. Chandra, S. K. Hui and A. A. Shaikh, Second order parallel tensors and Ricci solitons on (LCS)n-manifolds, Commun. Korean Math. Soc. 30 (2015), 123-130. https://doi.org/10.4134/CKMS.2015.30.2.123
  5. U. C. De and A. Sarkar, On three-dimensional quasi-Sasakian manifolds, SUT J. Math., 45 (2009), 59-71.
  6. U. C. De and A. Sarkar, On φ-Ricci symmetric Sasakian manifolds, Proceding of the Jangjeon Mathematical Society, 11 (2008), 47-52.
  7. U. C. De and A. K. Mondal, 3-dimensional quasi-Sasakian manifolds and Ricci solitons, SUT J. Math, 48 (1) (2012), 71-81.
  8. U. C. De and K. Mandal, Ricci solitons and gradient Ricci solitions on N(κ)-paracontact manifolds, J. of Math. Phy., Ana.,Geom. 15 (3) (2019), 307-320.
  9. D. Dey and P. Majhi, Almost Kenmotsu metric as a conformal Ricci soliton, Conf. Geom. and Dynamics 23, 105-116.
  10. T. Dutta and A. Bhattacharyya, Ricci soliton and conformal Ricci soliton in Lorentzian β-Kenmotsu manifold, Int. J. Math. Combin. 2 (2018), 1-12.
  11. T. Dutta, N. Basu and A. Bhattacharyya, Conformal Ricci soliton in Lorentzian α-Sasakian manifolds, Acta Univ. Palaiki. Olomue, Fac. rer. nat. Mathematica 55 (2) (2016), 57-70.
  12. T. Dutta, N. Basu and A. Bhattacharyya, Almost conformal Ricci solitons on 3-dimensional trans-Sasakian manifold, Hacettepe J. Math. and Stat. 45 (5) (2016), 1379-1392.
  13. A. E. Fischer, An introduction to conformal Ricci Flow, Class. Quantum Grav. 21 (2004), 171-218. https://doi.org/10.1088/0264-9381/21/3/011
  14. R. S. Hamilton, The Ricci flow on surfaces, Contemporary Mathematics 71 (1988), 237-261. https://doi.org/10.1090/conm/071/954419
  15. S. K. Hui, S. K. Yadav and A. Patra, Almost conformal Ricci solitons on f-Kenmotsu manifolds, Khayyam J. Math. 5 (1) (2019), 89-104.
  16. K. Kenmotsu, A class of almost contact Riemannian manifolds, Tohoku Math. J. 24 (1972), 93-103. https://doi.org/10.2748/tmj/1178241594
  17. A. K. Mondal and U. C. De, Second order parallel tensor on N(κ)-contact metric manifolds, Differential Geometry-Dynamical System, Vol. 12 (2010), 158-165.
  18. H. G. Nagaraja, D. L. Kiran Kumar and D. G. Prakasha, Da-Homothetic Deformation And Ricci solitons in (κ, µ)-contact metric manifolds, Konuralp J. of Math. 7 (1) (2019), 122-127.
  19. Z. Olszak, Locally conformal almost cosymplectic manifolds, Colloq. Math. 57 (1989), 73-87. https://doi.org/10.4064/cm-57-1-73-87
  20. Z. Olszak and R. Rosca, Normal locally conformal almost cosymplectic manifolds, Publ. Math. Debrecen, 39 (1991), 315-323.
  21. R. Sharma, Second order parallel tensor in real and complex space forms, Internat. J. Math. Sci. 12 (1989), 787-790. https://doi.org/10.1155/S0161171289000967
  22. R. Sharma, Second order parallel tensor on contact manifolds, Algebras Groups Geom. 7 (1990), 145-152.
  23. Venkatesha and G. Divyashree, Three dimensional f-Kenmotsu manifold satisfying certain curvature conditions, CUBO Math. J. 19 (1), 79-87. https://doi.org/10.4067/S0719-06462017000100005
  24. A. Yildiz, U. C. De and M. Turan, On 3-dimensional f-Kenmotsu manifolds and Ricci solitons, Ukrainain Math. J. 5 (2013), 620-628.