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Generalized Ricci Solitons on N(κ)-contact Metric Manifolds

  • Tarak Mandal (Department of Mathematics, University of Kalyani) ;
  • Urmila Biswas (Department of Mathematics, University of Kalyani) ;
  • Avijit Sarkar (Department of Mathematics, University of Kalyani)
  • Received : 2022.11.25
  • Accepted : 2023.06.01
  • Published : 2023.06.30

Abstract

In the present paper, we study generalized Ricci solitons on N(κ)-contact metric manifolds, in particular, we consider when the potential vector field is the concircular vector field. We also consider generalized gradient Ricci solitons, and verify our results with an example.

Keywords

Acknowledgement

The authors are 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., Springer-Verlag, Berlin-New York(1976).
  2. D. E. Blair, Two remarks on contact metric structure, Tohoku Math., J., 29(1977), 319-324. https://doi.org/10.2748/tmj/1178240602
  3. D. E. Blair, T. Koufogiorgos and B. J. Papantoniou, Contact metric manifolds satisfying a nullity condition, Israel J. Math., 91(1995), 189-214. https://doi.org/10.1007/BF02761646
  4. F. Brickell and K. Yano, Concurrent vector fields and Minkowski structure, Kodai Math. Sem. Rep., 26(1974), 22-28.
  5. U. C. De, A. Yildiz and S. Ghosh, On a class of N(κ)-contact metric manifolds, Math. Reports, 16(66)(2014), 207-217.
  6. G. Ghosh and U. C. De, Generalized Ricci solitons on K-contact manifolds, Math. Sci. Appl. E-Notes, 8(2)(2020), 165-169. https://doi.org/10.36753/mathenot.683478
  7. G. Ghosh and U. C. De, Generalized Ricci solitons on contact metric manifolds, Afr. Mat., 33(2022), 1-6. https://doi.org/10.1007/s13370-021-00941-2
  8. R. S. Hamilton, The Ricci flow on Surfaces, Contemp. Math., 71(1988), 237-262. https://doi.org/10.1090/conm/071/954419
  9. H. A. Kumara, D. M. Naik and V. Venkatesha, Geometry of generalized Ricci-type solitons on a class of Riemannian manifolds, J. Geom. Phys., 176(2022), 7pp.
  10. P. Nurowski and M. Randall, Generalized Ricci solitons, J. Geom. Anal., 26(2016), 1280-1345. https://doi.org/10.1007/s12220-015-9592-8
  11. A. Sarkar and A. Sardar, η-Ricci solitons on N(κ)-contact metric manifolds, Filomat, 35(11)(2021), 3879-3889. https://doi.org/10.2298/FIL2111879S
  12. S. Tanno, The topology of contact Riemannian manifolds, Illinois J. Math., 12(1968), 700-717. https://doi.org/10.1215/ijm/1256053971
  13. M. Turan, U. C. De and A. Yildiz, Ricci solitons and gradient Ricci solitons in three-dimensional trans-Sasakian manifolds, Filomat, 26(2)(2012), 363-370. https://doi.org/10.2298/FIL1202363T
  14. K. Yano, Integral formulas in Riemannian Geometry, Marcel Dekker, New York(1970).