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

Yıl 2021, Cilt: 50 Sayı: 3, 770 - 777, 07.06.2021

Sujit Ghosh U.c. De Ahmet Yıldız

https://doi.org/10.15672/hujms.785628

Cited By: 2

Öz

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.

Anahtar Kelimeler

almost quasi-Yamabe solitons, gradient almost quasi-Yamabe solitons, Kenmotsu manifolds

Kaynakça

• [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.