Open Access
Research Article
∗-η-Ricci Soliton within the Framework of Sasakian Manifold
*Santu DeyCorresponding authorsantu.mathju@gmail.comDepartment of MathematicsAsansol - 4Bidhan Chandra CollegeWest Bengal, 713303, IndiaView full profile → , Soumendu Roysoumendu1103mtma@gmail.comDepartment of MathematicsJadavpur UniversityKolkata, 700032, IndiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 08 Jun 2019
- Accepted:
- 03 Jul 2020
- Published Online:
- 07 Jan 2021
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- 1726037X.2020.1856339
- Pages:
- 163–181
Abstract
In this paper we study ∗-η-Ricci soliton on Sasakian manifolds. Here, we have discussed some curvature properties on Sasakian manifold admitting ∗-η-Ricci soliton. We have obtained some significant results on ∗-η-Ricci soliton in Sasakian manifolds satisfying R(ξ, X) · S = 0, S(ξ, X) · R = 0, P̄ (ξ, X) · S = 0, where P̄ is Pseudo-projective curvature tensor.The conditions for ∗-η-Ricci soliton on ϕ-conharmonically flat and ϕ-projectively flat Sasakian manifolds have been obtained in this article. Lastly, we have given an example of 5-dimensional Sasakian manifolds satisfying ∗-η-Ricci soliton.
References
- Adara M.Blaga, .
- Jong TaekCho, MakotoKimura, , Tohoku Mathematical Journal , Second Series , Vol. 61 , Number. 2 , 205 - 212 ( 2009 ).
- TamalikaDutta, ArindamBhattacharyya, SrabaniDebnath, , International J.Math. Combin ., Vol. 3 , 17 - 26 ( 2016 ).
- AmalenduGhosh and Dhriti SundarPatra, , International Journal of Geometric Methods in Modern Physics ,Vol. 15 , Number. 07 , 1850120, 1 - 23 ( 2018 ).
- THamada, , Tokyo J. Math . ( 2002 ), Vol. 25 , pp- 473 - 483 .
- R. S.Hamilton, , J.Differential Geom ., Vol. 17 , Number. 2 , 255 - 306 ( 1982 ).
- R. S.Hamilton, , Contemporary Mathematics , Vol. 71 , 237 – 261 ( 1988 ).
- Y.Ishii, On conharmonic transformations , Tensor N.S , Vol. 7 , 73 - 80 ( 1957 ).
- GKaimakamis, KPanagiotidou, , Journal of Geometry and Physics , Vol. 76 , 408 - 413 ( 2014 ).
- C.Ozgur, , Radovi Mathematicki , Vol. 12 , 99 - 106 ( 2003 ).
- B.Prasad, , Bull. Calcutta Math. Soc ., 94 , 163166 ( 2002 ).
- SoumenduRoy, Santu Dey, Arindam Bhattacharyya, Shyamal Kumar Hui, , arXiv:1909.01318v1 [math.DG](2019) .
- SoumenduRoy, ArindamBhattacharyya, , Jordan Journal of Mathematics and Statistics , Vol. 13 , Number 1 , 89 - 109 ( 2020 ).
- Mohd DanishSiddiqi, , International Journal of Maps in Mathematics , vol. 1 , Number. 1 , 15 - 34 ( 2018 ).
- AbhishekSingh, ShyamKishor, , Ser. Math. Inform ., Vol. 33 , Number 2 , 217230( 2018 ).
- STachibana, , Tohoku Math.J , Vol. 11 , Number 2 , 247 - 265 ( 1959 ).
- PeterTopping, , Cambridge University Press ( 2006 ).
- K.Yano, M.Kon, Series in Pure Mathematics , Vol. 3 ( 1984 ).
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