DOI QR코드

DOI QR Code

𝜂-RICCI SOLITONS ON KENMOTSU MANIFOLDS ADMITTING GENERAL CONNECTION

  • 투고 : 2020.05.13
  • 심사 : 2020.12.08
  • 발행 : 2020.12.30

초록

The object of the present paper is to study 𝜂-Ricci soliton on Kenmotsu manifold with respect to general connection.

키워드

참고문헌

  1. A. Basari, C. Murathan, On generalised 𝜙- reccurent Kenmotsu manifolds, SDU Fen Dergisi 3 (1) (2008), 91-97.
  2. K. K. Baishya & P. R. Chowdhury, On generalized quasi-conformal N(κ, μ)-manifolds, Commun. Korean Math. Soc., 31 (1) (2016), 163-176. https://doi.org/10.4134/CKMS.2016.31.1.163
  3. A. Biswas and K.K. Baishya, Study on generalized pseudo (Ricci) symmetric Sasakian manifold admitting general connection, Bulletin of the Transilvania University of Brasov, 12 (2) (2019), https://doi.org/10.31926/but.mif.2019.12.61.2.4.
  4. A. Biswas and K.K. Baishya, A general connection on Sasakian manifolds and the case of almost pseudo symmetric Sasakian manifolds, Scientific Studies and Research Series Mathematics and Informatics, 29 (1) (2019).
  5. A. Biswas, S. Das and K.K. Baishya,On Sasakian manifolds satisfying curva-ture restrictions with respect to quarter symmetric metric connection, Scientific Studies and Research Series Mathematics and Informatics, 28 (1) (2018), 29-40.
  6. D. E. Blair, Riemannian Geometry of Contact and Symplectic Manifolds, Birkhauser, Boston, 2002.
  7. A. M. Blaga, 𝜂-Ricci solitons on Lorentzian para-Sasakian manifolds, Filomat 30 (2) (2016), 489-496. https://doi.org/10.2298/FIL1602489B
  8. K.Yano and S. Bochner, Curvature and Betti numbers, Annals of Mathematics Studies, Princeton University Press,32 (1953).
  9. K. K. Baishya and P. R. Chowdhury, η-Ricci solitons in (LCS)n-manifolds, Bull. Transilv. Univ. Brasov, 58 (2) (2016), 1-12.
  10. L. P.Eisenhart, Riemannian Geometry, Princeton University Press, (1949).
  11. Golab, S., On semi-symmetric and quarter-symmetric linear connections, Tensor(N.S.) 29 (1975), 249-254.
  12. Y.Ishii, On conharmonic transformations, Tensor (N.S.),7 (1957), 73-80.
  13. J. T. Cho and M. Kimura, Ricci solitons and real hypersurfaces in a complex space form, Tohoku Math. J. 61 (2) (2009), 205-212. https://doi.org/10.2748/tmj/1245849443
  14. K. Kenmotsu, A class of almost contact Riemannian manifolds, Tohoku Math. J. 24 (1972), 93-103. https://doi.org/10.2748/tmj/1178241594
  15. K. K. Baishya, More on η-Ricci solitons in (LCS)n-manifolds, Bulletin of the Transilvania University of Brasov, Series III, Maths, Informatics, Physics., 60 (1), (2018), 1-10
  16. K. K. Baishya, Ricci Solitons in Sasakian manifold, Afr. Mat. 28 (2017), 1061-1066, DOI: 10.1007/s13370-017-0502-z.
  17. K. K. Baishya, P. R. Chowdhury, M. Josef and P. Peska, On almost generalized weakly symmetric Kenmotsu manifolds, Acta Univ. Palacki. Olomuc., Fac. rer. nat., Mathematica, 55 (2) (2016), 5-15.
  18. D. G. Prakasha and B. S. Hadimani, η-Ricci solitons on para-Sasakian manifolds, J. Geom. 108 (2017), 383-392. https://doi.org/10.1007/s00022-016-0345-z
  19. G. Perelman, The entropy formula for the Ricci flow and its geometric applications, http://arXiv.org/abs/math/0211159, (2002), 1-39.
  20. G. Perelman, Ricci flow with surgery on three manifolds, http://arXiv.org/abs/math/0303109, (2003), 1-22.
  21. G.P. Pokhariyal and R.S. Mishra, Curvature tensors and their relativistic significance, Yokohama Math. J. 18 (1970), 105-108.
  22. G.P. Pokhariyal and R.S. Mishra, Curvature tensors and their relativistic significance II, Yokohama Math. J. 19 (2) (1971), 97-103.
  23. R. Sharma, Certain results on κ-contact and (κ,µ)-contact manifolds, J. Geom. 89 (2008), 138-147. https://doi.org/10.1007/s00022-008-2004-5
  24. R. S. Hamilton, The Ricci flow on surfaces, Mathematics and general relativity, Contemp. Math., American Math. Soc., 71 (1988), 237-262. https://doi.org/10.1090/conm/071/954419
  25. S. Deshmukh, H. Alodan and H. Al-Sodais, A note on Ricci solitons, Balkan J. Geom. Appl. 16 (2011), 48-55.
  26. Schouten, J. A. and Van Kampen, E. R., Zur Einbettungs-und Krummungstheorie nichtholonomer, Gebilde Math. Ann. 103 (1930), 752-783. https://doi.org/10.1007/BF01455718
  27. S. M. Webster, h Pseudo hermitian structures on a real hypersurface, J. Differ. Geom. 13 (1978), 25-41. https://doi.org/10.4310/jdg/1214434345
  28. S. Eyasmin, P. Roy Chowdhury and K. K. Baishya, η-Ricci solitons in Kenmotsu manifolds, Honam Mathematical J 40 (2) (2018), 383-392.
  29. S. Tanno, The automorphism groups of almost contact Riemannian manifold, Tohoku Math. J. 21 (1969), 21-38. https://doi.org/10.2748/tmj/1178243031
  30. V. F. Kirichenko, On the geometry of Kenmotsu manifolds, Dokl. Akad. Nauk, Ross. Akad. Nauk 380 (2001), 585-587.
  31. Yano, K. and Imai T., Quarter-symmetric metric connections and their curvature tensors, Tensor (N.S.) 38 (1982), 13-18.
  32. Yano, K., On semi-symmetric connection. Revue Roumanie de Mathematiques Pures et appliquees, 15(1970), 1579-1586.
  33. S. Zamkovoy, Canonical connections on paracontact manifolds. Ann. Global Anal. Geom. 36 (1) (2008), 37-60. https://doi.org/10.1007/s10455-008-9147-3