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## A note on almost quasi Yamabe solitons and gradient almost quasi Yamabe solitons

#### Sujit GHOSH [1] , U.c. DE [2] , Ahmet YILDIZ [3]

In this article, we characterize almost quasi-Yamabe solitons and gradient almost quasi-Yamabe solitons in context of three dimensional Kenmotsu manifolds. It is proven that if the metric of a three dimensional Kenmotsu manifold admits an almost quasi-Yamabe soliton with soliton vector field $W$ then the manifold is of constant sectional curvature $-1$, but the converse is not true has been shown by a concrete example, under the restriction $\phi W\neq 0$. Next we consider gradient almost quasi-Yamabe solitons in a three dimensional Kenmotsu manifold.
almost quasi-Yamabe solitons, gradient almost quasi-Yamabe solitons, Kenmotsu manifolds
• [1] E. Barbosa and E. Ribeiro, On conformal solutions of the Yamabe flow, Arch. Math. 101, 79–89, 2013.
• [2] A.M. Blaga, A note on warped product almost quasi-Yamabe solitons, Filomat 33, 2009–2016, 2019.
• [3] D.E. Blair, Contact manifolds in Riemannian geometry, Lect. Notes Math. 509, 1976.
• [4] X. Chen, Almost quasi-Yamabe solitons on Almost cosymplectic manifolds, Int. J. Geom. Methods Mod. Phys. 17, 2050070, 2020.
• [5] C. Dey and U.C. De, A note on quasi-Yamabe solitons on contact metric manifolds, J. Geom. 111, 1–7, 2020.
• [6] A. Ghosh, Yamabe soliton and quasi Yamabe soliton on Kenmotsu manifold, Math. Slovaca 70, 151–160, 2020.
• [7] R.S. Hamilton, The Ricci flow on surfaces, Mathematics and General Relativity, Contemp. Math. 71, 237–262, 1988.
• [8] G. Huang and H. Li, On a classification of the quasi-Yamabe gradient solitons, Meth- ods. Appl. Anal. 21, 379–390, 2014.
• [9] D. Janssens and L. Vanhecke, Almost contact structures and curvature tensors, Kodai Math. J. 4, 1–27, 1981.
• [10] K. Kenmotsu, A class of almost comtact Riemannian manifolds, Math. Ann. 219, 93–103, 1972.
• [11] S. Lie, Theorie der Transformationgruppen, 2, Leipzig, Tenbuer, 1890.
• [12] V. Pirhadi and A. Razavi, On the almost quasi-Yamabe solitons, Int. J. Geom. Meth- ods Mod. Phys. 14, 1750161, 2017.
• [13] G. Pitis, A remark on Kenmotsu manifolds, Bull. Univ. Brasov Ser. C. 30, 31–32, 1988.
• [14] T. Seko and S. Maeta, Classifications of almost Yamabe solitons in Euclidean spaces, J. Geome. Phys. 136, 97–103, 2019.
• [15] S. Tanno, The automorphism groups of almost contact Riemannian manifolds, Tohoku Math. J. 21, 21–38, 1969.
• [16] Y. Wang, Yamabe solitons on three-dimensional Kenmotsu manifolds, Bull. Belg. Math. Soc. Simon Stevin 23, 345–355, 2016.
• [17] K. Yano, Integral formulas in Riemannian geometry, Marcel Dekker, New York, 1970.
Primary Language en Mathematics Mathematics Orcid: 0000-0001-5726-8954Author: Sujit GHOSHInstitution: Krishnagar Government CollegeCountry: India Orcid: 0000-0002-8990-4609Author: U.c. DEInstitution: University of CalcuttaCountry: Turkey Orcid: 0000-0002-9799-1781Author: Ahmet YILDIZ (Primary Author)Institution: INONU UNIVERSITYCountry: Turkey Publication Date : June 7, 2021
 Bibtex @research article { hujms785628, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2021}, volume = {50}, pages = {770 - 777}, doi = {10.15672/hujms.785628}, title = {A note on almost quasi Yamabe solitons and gradient almost quasi Yamabe solitons}, key = {cite}, author = {Ghosh, Sujit and De, U.c. and Yıldız, Ahmet} } APA Ghosh, S , De, U , Yıldız, A . (2021). A note on almost quasi Yamabe solitons and gradient almost quasi Yamabe solitons . Hacettepe Journal of Mathematics and Statistics , 50 (3) , 770-777 . DOI: 10.15672/hujms.785628 MLA Ghosh, S , De, U , Yıldız, A . "A note on almost quasi Yamabe solitons and gradient almost quasi Yamabe solitons" . Hacettepe Journal of Mathematics and Statistics 50 (2021 ): 770-777 Chicago Ghosh, S , De, U , Yıldız, A . "A note on almost quasi Yamabe solitons and gradient almost quasi Yamabe solitons". Hacettepe Journal of Mathematics and Statistics 50 (2021 ): 770-777 RIS TY - JOUR T1 - A note on almost quasi Yamabe solitons and gradient almost quasi Yamabe solitons AU - Sujit Ghosh , U.c. De , Ahmet Yıldız Y1 - 2021 PY - 2021 N1 - doi: 10.15672/hujms.785628 DO - 10.15672/hujms.785628 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 770 EP - 777 VL - 50 IS - 3 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.785628 UR - https://doi.org/10.15672/hujms.785628 Y2 - 2020 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics A note on almost quasi Yamabe solitons and gradient almost quasi Yamabe solitons %A Sujit Ghosh , U.c. De , Ahmet Yıldız %T A note on almost quasi Yamabe solitons and gradient almost quasi Yamabe solitons %D 2021 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 50 %N 3 %R doi: 10.15672/hujms.785628 %U 10.15672/hujms.785628 ISNAD Ghosh, Sujit , De, U.c. , Yıldız, Ahmet . "A note on almost quasi Yamabe solitons and gradient almost quasi Yamabe solitons". Hacettepe Journal of Mathematics and Statistics 50 / 3 (June 2021): 770-777 . https://doi.org/10.15672/hujms.785628 AMA Ghosh S , De U , Yıldız A . A note on almost quasi Yamabe solitons and gradient almost quasi Yamabe solitons. Hacettepe Journal of Mathematics and Statistics. 2021; 50(3): 770-777. Vancouver Ghosh S , De U , Yıldız A . A note on almost quasi Yamabe solitons and gradient almost quasi Yamabe solitons. Hacettepe Journal of Mathematics and Statistics. 2021; 50(3): 770-777. IEEE S. Ghosh , U. De and A. Yıldız , "A note on almost quasi Yamabe solitons and gradient almost quasi Yamabe solitons", Hacettepe Journal of Mathematics and Statistics, vol. 50, no. 3, pp. 770-777, Jun. 2021, doi:10.15672/hujms.785628

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