Research Article
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Year 2021, Volume: 50 Issue: 3, 770 - 777, 07.06.2021
https://doi.org/10.15672/hujms.785628

Abstract

References

  • [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.

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

Year 2021, Volume: 50 Issue: 3, 770 - 777, 07.06.2021
https://doi.org/10.15672/hujms.785628

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.

References

  • [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.
There are 17 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Sujit Ghosh 0000-0001-5726-8954

U.c. De 0000-0002-8990-4609

Ahmet Yıldız 0000-0002-9799-1781

Publication Date June 7, 2021
Published in Issue Year 2021 Volume: 50 Issue: 3

Cite

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. 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. June 2021;50(3):770-777. doi:10.15672/hujms.785628
Chicago Ghosh, Sujit, U.c. De, and Ahmet Yıldız. “A Note on Almost Quasi Yamabe Solitons and Gradient Almost Quasi Yamabe Solitons”. Hacettepe Journal of Mathematics and Statistics 50, no. 3 (June 2021): 770-77. https://doi.org/10.15672/hujms.785628.
EndNote Ghosh S, De U, Yıldız A (June 1, 2021) A note on almost quasi Yamabe solitons and gradient almost quasi Yamabe solitons. Hacettepe Journal of Mathematics and Statistics 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, 2021, doi: 10.15672/hujms.785628.
ISNAD Ghosh, Sujit et al. “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.
JAMA 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;50:770–777.
MLA Ghosh, Sujit et al. “A Note on Almost Quasi Yamabe Solitons and Gradient Almost Quasi Yamabe Solitons”. Hacettepe Journal of Mathematics and Statistics, vol. 50, no. 3, 2021, pp. 770-7, doi:10.15672/hujms.785628.
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):770-7.