Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
권호 표지
DOI QR코드

DOI QR Code

A NOTE ON (𝑘, 𝜇)'-ALMOST KENMOTSU MANIFOLDS

  • Yadav, Sunil Kumar (Department of Applied Science, Faculty of Mathematics, United College of Engineering & Research, UPSIDC Industrial Area) ;
  • Mandal, Yadab Chandra (Department of Mathematics, The University of Burdwan) ;
  • Hui, Shyamal Kumar (Department of Mathematics, The University of Burdwan)
  • Received : 2021.01.07
  • Accepted : 2021.07.09
  • Published : 2021.12.25
Download PDF
⟨ Previous Next ⟩

Abstract

The present paper deals with the study of generalized quasi-conformal curvature tensor inside the setting of (𝑘, 𝜇)'-almost Kenmotsu manifold with respect to 𝜂-Ricci soliton. Certain consequences of these curvature tensor on such manifold are likewise displayed. Finally, we illustrate some examples based on this study.

Keywords

Acknowledgement

The authors are thankful to the referees for their valuable suggestions towards to the improvement of the paper.

References

  1. D. E. Blair, T. Koufogiorgos, and B. J. Papantoniou, Contact metric manifolds satisfying a nulitty condition, Israel. J. Math., 91 (1995), 189-214. https://doi.org/10.1007/BF02761646
  2. D. E. Blair, Contact Manifolds in Reimannian Geometry, Lecture Notes in Mathematics 509, Springer-Verlag, Berlin, (1976).
  3. D. E. Blair, Reimannian Geometry of Contact and Sympletic Manifolds, Progress in Mathematics 203, Birkhauser, Basel, (2010).
  4. K. K. Baishya and P. R. Chowdhury, On generalized quasi-conformal N(κ, µ)-manifolds, Commun. Korean Math. Soc.,31 (2016), 163-176. https://doi.org/10.4134/CKMS.2016.31.1.163
  5. W. G. Boskoff, M. Crasmareanu and L. I. Piscoran, Tzitzeica equations and Tzitzeica surfaces in separable cordinate systems and the Ricci flow tensor field, Carpathian J. Math., 33(2) (2017), 141-151. https://doi.org/10.37193/CJM.2017.02.01
  6. J. T. Cho and M. Kimura, Ricci solitons and real hypersurfaces in a complex space-form, Tohoku Math. J., 61 (2009), 205-212. https://doi.org/10.2748/tmj/1245849443
  7. C. Calin and C. Crasmareanu, From the Eisenhart problem to the Ricci solitons in f-Kenmotau manifolds, Bull. Malays. Math. Sci. Soc., 339(3) (2010), 361-368.
  8. M. Crasmareanu, New properties of Euclidean Killing tensors of rank two, J. Geom. Symmetry Phys., 51, (2019), 1-7. https://doi.org/10.7546/jgsp-51-2019-1-7
  9. B. Y. Chen and S. Deshmukh, Geometry of compact shrinking Ricci solitons, Balkan J. Geom. Appl., 19 (2014), 1-12.
  10. G. Dileo and A. M. Pastore, Almost Kenmotsu manifolds and nullity distributions, J. Geom. 93 (2009), 46-61. https://doi.org/10.1007/s00022-009-1974-2
  11. G. Dileo and A. M. Pastore, Almost Kenmotsu manifolds with a condition of η-parallelism, Differential Geom. Appl. 27 (2009), 671-679. https://doi.org/10.1016/j.difgeo.2009.03.007
  12. G. Dileo and A. M. Pastore, Almost Kenmotsu manifolds and local symmetry, Bull. Belg. Math. Soc. Simon Stevin 14 (2007), 343-354.
  13. S. Deshmukh, Jacobi type vector fields on Ricci solitons, Bull. Math. Soc. Sci. Math, Roumanie, 1, 55, 103, (2012), 41-50.
  14. L. P. Eisenhart,Riemannian Geometry, Princeton University Press,(1949).
  15. A. Gray, Spaces of constancy of curvature operators, Proc. Amer. Math. Soc., 17 (1966), 897-902. https://doi.org/10.1090/S0002-9939-1966-0198392-4
  16. R. S. Hamilton The Ricci flow on surfaces, Contemporary Mathematics, 71 (1988), 237-262. https://doi.org/10.1090/conm/071/954419
  17. S. K. Hui, S. K. Yadav and S. K. Chaubey, η-Ricci soliton on 3-dimensional f-Kenmotsu manifolds, An International Journal, Applications and Applied Mathematics, 13, 2, (2018), 933-951.
  18. S. K. Hui and D. Chakraborty, Generalized Sasakian-space-forms and Ricci almost solitons with a conformal Killing vector field, New Trends in Math. Sciences, 4 (2016), 263-269. https://doi.org/10.20852/ntmsci.2016320381
  19. S. K. Hui and D. Chakraborty, Para-Sasakian manifolds and Ricci solitons, Ilirias J. of Math., 6 (2017), 25-34.
  20. S. K. Hui and D. Chakraborty, Ricci almost solitons on Concircular Ricci pseudosymmetric β-Kenmotsu manifolds, Hacettepe Journal of Mathematics and Statistics, 47(3) (2018), 579-587.
  21. S. K. Hui and A. Patra, Ricci almost solitons on Riemannian manifolds, Tamsui Oxford J. Information and Mathematical Sciences, 31(2) (2017), 1-8.
  22. S. K. Hui, R. Prasad and D. Chakraborty, Ricci solitons on Kenmotsu manifolds with respect to quarter symmetric non-metric ϕ-connection, Ganita, 67 (2017), 195-204.
  23. S. K. Hui, S. Uddin and D. Chakraborty, Generalized Sasakian-space-forms whose metric is η-Ricci almost solitons, Differential Geometry and Dynamical Systems, 19 (2017), 45-55.
  24. S. K. Hui, S. K. Yadav and A. Patra, Almost conformal Ricci solitons on f-Kenmotsu manifolds, Khayyam J. Math., 5 (2019), 84-104.
  25. Y. Ishii, On conharmonic transformations, Tensor, N. S., 7 (1957), 73-80.
  26. T. Ivey, Ricci solitons on compact 3-manifolds, Different. Geom. Appl., 3 (1993), 301-307. https://doi.org/10.1016/0926-2245(93)90008-O
  27. K. Kenmotsu, A class of almost contact Riemannian manifolds, Tohoku Mathematical Journal 24, 1 (1972), 93-103. https://doi.org/10.2748/tmj/1178241594
  28. A. M. Pastore and V. Saltarelli, Almost Kenmotsu manifolds with conformal Reeb foliation, Bull. Belg. Math. Soc. Simon Stevin, 21 (2012), 343-354.
  29. A. M. Pastore and V. Saltarelli, Generalized nullity distribution on an almost Kenmotsu manifolds, J. Geom., 4 (2011), 168-183.
  30. G. P. Pokhariyal and R. S. Mishra, Curvature tensor and their relativistic significance II, Yokohama Math. J.,19 (1971), 97-103.
  31. S. Tanno, Some differential equation on Reimannian manifolds, J. Math. Soc. Japan 30 (1978), 509-531. https://doi.org/10.2969/jmsj/03030509
  32. Y. Wang and X. Liu, Remannian semisymmetric almost Kenmotsu manifolds and nullity distributions, Ann. Polon. Math. 112 (2014), 37-46. https://doi.org/10.4064/ap112-1-3
  33. Y. Wang and X. Liu, On ϕ-recurrent almost kenmotsu manifolds, Kuwait J. Sci., 42 (2015), 65-77.
  34. Y. Wang and X. Liu, Second order parrallel tensors on almost Kenmotsu manifolds satisfying the nullity distributions, Filomat, 28 (2014), 839-847. https://doi.org/10.2298/FIL1404839W
  35. K. Yano and S. Sawaki, Riemannian manifolds admitting a conformal transformation group, J. Diff. Geom., 2 (1968), 161-184.
  36. K. Yano and S. Bochner, Curvature and Betti numbers, Annals of Math Studies 32, Princeton University Press, (1953).
  37. S. K. Yadav and M. D. Sidhiqui, On Almost Kenmotsu (κ, µ, ν)-spaces, Differential Geometry - Dynamical Systems, 23, (2021), 263-282.
  38. S. K. Yadav, S. K. Chaubey and D. L. Suthar, Certain geometric properties of η-Ricci soliton on η-Einstein para-Kenmotsu manifolds, Palestine Journal of Mathematics, 9, 1, (2020), 237-244.
  39. S. K. Yadav, A. Kushwaha and D. Narain, Certain results for η-Ricci soliton and Yamabe soliton on quasi-Sasakian 3-manifolds, Cubo A mathematical Journal, 21, 2, (2019), 77-98. https://doi.org/10.4067/S0719-06462019000200077
  40. Sunil Kumar Yadav, Ricci solitons on para-Kaehler manifolds, Extracta Mathematikae, 34,2, (2019), 269-284.
  41. S. K. Yadav, S. K.Chaubey and D. L. Suthar, Some results of η-Ricci soliton on (LCS)n-manifolds, Surveys in Mathematics and its Applications, 13, (2018), 237-250.
  42. S. K. Yadav, S. K. Chaubey and D. L. Suthar, Certain results on Almost Kenmotsu (κ, µ, ν)-spaces, Konuralp Journal of Mathematics, 6, 1, (2018), 128-133.
  43. S. K. Yadav, S. K. Chaubey and D. L . Suthar, Some geometric properties of η-Ricci soliton and gradient Ricci soliton on (LCS)2n+1-manifolds, Cubo A Mathematical Journal, 19, 2, (2017), 33-48. https://doi.org/10.4067/S0719-06462017000200033