DOI QR코드

DOI QR Code

𝜂-Einstein Solitons on (𝜀)-Kenmotsu Manifolds

  • Received : 2019.10.09
  • Accepted : 2020.06.29
  • Published : 2020.12.31

Abstract

The objective of this study is to investigate 𝜂-Einstein solitons on (𝜀)-Kenmotsu manifolds when the Weyl-conformal curvature tensor satisfies some geometric properties such as being flat, semi-symmetric and Einstein semi-symmetric. Here, we discuss the properties of 𝜂-Einstein solitons on 𝜑-symmetric (𝜀)-Kenmotsu manifolds.

Keywords

Acknowledgement

The authors are thankful to the referee's for their valuable comments and suggestions for the improvement of the paper.

References

  1. C. S. Bagewadi, G. Ingalahalli and S. R. Ashoka, A study on Ricci solitons in Kenmotsu manifolds, ISRN Geom., (2013), Art. ID 412593, 6 pp.
  2. A. Bejancu and K. L. Duggal, Real hypersurfaces of indefinite Kaehler manifolds, Int. J. Math. Math. Sci., 16(3)(1993), 545-556. https://doi.org/10.1155/S0161171293000675
  3. A. M. Blaga, η-Ricci solitons on para-Kenmotsu manifolds, Balkan J. Geom. Appl., 20(2015), 1-13.
  4. A. M. Blaga, On gradient η-Einstein solitons, Kragujevac J. Math., 42(2)(2018), 229-237. https://doi.org/10.5937/KgJMath1802229B
  5. A. M. Blaga, S. Y. Perktas, B. L. Acet and F. E. Erdogan, η-Ricci solitons in (ϵ)-almost paracontact metric manifolds, Glas. Mat. Ser. III, 53(73)(2018), 205-220. https://doi.org/10.3336/gm.53.1.14
  6. D. E. Blair, Contact manifolds in Riemannian geometry, Lecture Note in Mathematics 509, Springer-Verlag Berlin-New York, 1976.
  7. G. Catino and L. Mazzieri, Gradient Einstein solitons, Nonlinear Anal., 132(2016), 66-94. https://doi.org/10.1016/j.na.2015.10.021
  8. S. K. Chaubey and R. H. Ojha, On the m-projective curvature tensor of a Kenmotsu manifold, Differ. Geom. Dyn. Syst., 12(2010), 52-60.
  9. 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
  10. U. C. De and A. Sarkar, On ϵ-Kenmotsu manifold, Hardonic J., 32(2)(2009), 231-242.
  11. R. S. Hamilton, The Ricci flow on surfaces, Mathematics and general relativity(Santa Cruz. CA, 1986), 237-262, Contemp. Math. 71, Amer. Math. Soc., 1988.
  12. J. B. Jun, U. C. De and G. Pathak, On Kenmotsu manifolds, J. Korean Math. Soc., 42(3)(2005), 435-445. https://doi.org/10.4134/JKMS.2005.42.3.435
  13. K. Kenmotsu, A class of almost contact Riemannian manifold, Tohoku Math. J., 24(1972), 93-103. https://doi.org/10.2748/tmj/1178241594
  14. H. Levy, Symmetric tensors of the second order whose covariant derivatives vanish, Ann. Math., 27(2)(1925), 91-98. https://doi.org/10.2307/1967964
  15. H. G. Nagaraja and C. R. Premalatha, Ricci solitons in Kenmotsu manifolds, J. Math. Anal., 3(2)(2012), 18-24.
  16. R. Sharma, Certain results on K-contact and (k, μ)-contact manifolds, J. Geom., 89(1-2)(2008), 138-147. https://doi.org/10.1007/s00022-008-2004-5
  17. M. D. Siddiqi, η-Einstein solitons in a δ-Lorentzian trans Sasakian manifolds, Mathematical Advances in Pure and Applied Sciences, 1(1)(2018), 27-38.
  18. M. D. Siddiqi, η-Einstein solitons in an (ε)-Kenmotsu manifolds with a semi-symmetric metric connection, Annales. Univ. Sci. Budapest, 62(2019), 5-24.
  19. X. Xufeng and C. Xiaoli, Two theorems on ϵ-Sasakian manifolds, Int. J. Math. Math. Sci., 21(2)(1998), 249-254. https://doi.org/10.1155/S0161171298000350