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Dergiler / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2021 / Cilt: 70 - Sayı: 2

Cotton tensor on Sasakian 3-manifolds admitting eta-Ricci solitons

Debabrata KAR
Pradip MAJHİ
Sayfa
569–581
Yayın Tarihi
2021-12-31
DOI
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Finally, we give an important remark.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:The object of the present paper is to characterize Cotton tensor on a 3-dimensional Sasakian manifold admitting $\eta$-Ricci solitons.
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Temel Bulgular & Veri:After introduction, we study 3-dimensional Sasakian manifolds and introduce a new notion, namely, Cotton pseudo-symmetric manifolds.
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Sonuç & Katkı:Finally, we give an important remark.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Einstein manifold · Ricci soliton · $\eta$-Ricci soliton

Abstract

The object of the present paper is to characterize Cotton tensor on a 3-dimensional Sasakian manifold admitting $\eta$-Ricci solitons. After introduction, we study 3-dimensional Sasakian manifolds and introduce a new notion, namely, Cotton pseudo-symmetric manifolds. Next we deal with the study Cotton tensor on a Sasakian 3-manifold admitting $\eta$-Ricci solitons. Among others we prove that such a manifold is a manifold of constant scalar curvature and Einstein manifold with some appropriate conditions. Also, we classify the nature of the soliton metric. Finally, we give an important remark.

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Bu Makaleye Atıf Yap

KAR, D., MAJHİ, P. (2021). Cotton tensor on Sasakian 3-manifolds admitting eta-Ricci solitons. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Cilt: 70 - Sayı: 2, 569–581. https://ajindex.com/articles/746684

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Kaynakça (19)

  1. Alegre, P. and Carriazo, A., Semi-Riemannian generalized Sasakian space forms, Bulletin of the Malaysian Mathematical Sciences Society, 41 (2018), 1-14. DOI:10.1007/ s40840-015-0215-0.
  2. Ayar, G. and Yildirim, M., η-Ricci solitons on nearly Kenmotsu manifolds, Asian-European Journal of Mathematics, 12(6) (2019), 2040002 (8pp.). DOI:10.1142/S1793557120400021 Blaga, A. M., η-Ricci solitons on Lorentzian para-Sasakian manifolds, Filomat, 30(2) (2016), 489-496.
  3. Blaga, A. M., η-Ricci solitons on para-Kenmotsu manifolds, Balkan J. Geom. Appl., 20 (2015), 1-13.
  4. Blaga, A. M., Torse-forming η-Ricci solitons in almost paracontact η-Einstein geometry, Filomat, 31(2) (2017), 499-504.
  5. Boeckx, E., Kowalski, O. and Vanhecke, L., Riemannian Manifolds of Conullity Two, Singapore World Sci. Publishing, 1996.
  6. Blair, D. E., Lecture Notes in Mathematics, 509, Springer-Verlag Berlin, 1976.
  7. Blair, D. E., Riemannian Geometry of Contact and Symplectic Manifolds, Birkhäuser, Boston, 2010.
  8. Blair, D. E., Koufogiorgos, T. and Sharma, R., A classification of 3-dimensional contact metric manifolds with Qϕ = ϕQ, Kodai Math. J., 13 (1990), 391-401.
  9. Cartan, E., Sur une classe remarqable d'espaces de Riemann, Bull. Soc. Math. France., 54 (1926), 214-264.
  10. Cho, J. T. and Kimura, M., Ricci solitons and real hypersurfaces in a complex space form, Tohoku Math. J., 61(2) (2009), 205-212.
  11. Calin, C. and Crasmareanu, M., From the Eisenhart problem to Ricci solitons in f-Kenmotsu manifolds, Bull. Malays. Math. Soc., 33(3) (2010), 361-368.
  12. Chave, T. and Valent, G., Quasi-Einstein metrics and their renoirmalizability properties, Helv. Phys. Acta., 69 (1996), 344-347.
  13. Chave, T. and Valent, G., On a class of compact and non-compact quasi-Einstein metrics and their renoirmalizability properties, Nuclear Phys. B., 478 (1996), 758-778.
  14. Deshmukh, S., Jacobi-type vector fields on Ricci solitons, Bull. Math. Soc. Sci. Math. Roumanie, 55(103) 1 (2012), 41-50.
  15. Deshmukh, S., Alodan, H. and Al-Sodais, H., A Note on Ricci Soliton, Balkan J. Geom. Appl., 16(1) (2011), 48-55.
  16. Hamilton, R. S., The Ricci flow on surfaces, mathematics and general relativity, (Santa Cruz, CA, 1986), 237-262. Contemp. Math., 71, American Math. Soc., 1988.
  17. Hamilton, R. S., Three manifolds with positive Ricci curvature, J. Di¤ erential Geom., 17 (1982), 255-306.
  18. Ivey, T., Ricci solitons on compact 3-manifolds, Diff. Geom. Appl., 3 (1993), 301-307.
  19. Kar, D., Majhi, P. and De, U. C., η-Ricci solitons on 3-dimensional N(k)-contact metric manifold