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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2021 / Cilt: 50 - Sayı: 3

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

Sujit GHOSH
Uday CHAND DE
Ahmet YILDIZ
Sayfa
770–777
Yayın Tarihi
2022-10-18
DOI
—
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Next we consider gradient almost quasi-Yamabe solitons in a three dimensional Kenmotsu manifold.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this article, we characterize almost quasi-Yamabe solitons and gradient almost quasi-Yamabe solitons in context of three dimensional Kenmotsu manifolds.
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Temel Bulgular & Veri: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 $\phi W\neq 0$.
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Sonuç & Katkı:Next we consider gradient almost quasi-Yamabe solitons in a three dimensional Kenmotsu manifold.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:almost quasi-Yamabe solitons · gradient almost quasi-Yamabe solitons · Kenmotsu manifolds

Abstract

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.

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Bu Makaleye Atıf Yap

GHOSH, S., DE, U. C., YILDIZ, A. (2022). A note on almost quasi Yamabe solitons and gradient almost quasi Yamabe solitons. Hacettepe Journal of Mathematics and Statistics, Cilt: 50 - Sayı: 3, 770–777. https://ajindex.com/articles/529533

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Kaynakça (17)

  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.