Abstract
The goal of the current paper is to characterize paracontact metric manifolds conceding \(\delta \)-almost Yamabe solitons. A few fascinating results of such solitons are established. Specifically, we classify \(\delta \)-almost Yamabe solitons on \((k,\mu )\) and N(k)-paracontact metric manifolds.
Similar content being viewed by others
References
Blaga, A.M.: A note on warped product almost quasi-Yamabe solitons. Filomat 33, 2009–2016 (2019)
Calvaruso, G.: Homogeneous paracontact metric three-manifolds. Ill. J. Math. 55, 697–718 (2011)
Calviño-Louza, E., Seone-Bascoy, J., Vázquez-Abal, M.E., Vázquez-Lorenzo, R.: Three-dimensional homogeneous Lorentzian Yamabe solitons. Abh. Math. Semin. Univ. Hambg. 82, 193–203 (2012)
Cappelletti-Montano, B., Erken, I.K., Murathan, C.: Nullity conditions in paracontact geometry. Differ. Geom. Appl. 30, 665–693 (2012)
Chen, B.Y., Desmukh, S.: Yamabe and quasi-Yamabe solitons on Euclidean submanifolds. Mediterr. J. Math. 15(5), article 194 (2018)
Chen, X.M.: The \(k\)-almost Yamabe solitons and contact metric manifolds. Rocky Mountain J. Math. 51, 125–137 (2021)
Chen, X.M.: Almost quasi-Yamabe solitons on almost cosymplectic manifolds. Int. J. Geom. Methods Mod. Phys. 17(05), 2050070 (2020)
Desmukh, S., Chen, B.Y.: A note on Yamabe solitons. Balkan J. Geom. Appl. 23, 37–43 (2018)
Hamilton, R.: The Ricci flow on surface. Contemp. Math. 71, 237–262 (1988)
Hinterleitner, I., Volodymyr, A.K.: \(\phi (Ric)\)-vector fields in Riemannian spaces. Archivum Math. (Brno) 44, 385–390 (2008)
Kaneyuki, S., Williams, F.L.: Almost paracontact and parahodge structures on manifolds. Nagoya Math. J. 99, 173–177 (1985)
Kupeli, E. I.: Yamabe soliton on three-dimensional para-Sasakain manifolds. arXiv:1708.04882v1
Obata, M.: Certain conditions for a Riemannian manifold to be isometric with a sphere. J. Math. Soc. Jpn. 14, 333–340 (1962)
Pan, Q., Liu, X.: A classification of 3-dimensional paracontact metric manifolds with \(\phi l=l\phi \). J. Math. Res. Appl. 38, 509–522 (2018)
Pirhadi, V., Razavi, A.: On the almost quasi-Yamabe solitons. Int. J. Geom. Methods Mod. Phys. 14, 1750161 (2017)
Prakasha, D.G., Mirji, K.K.: On \(\phi \)-symmetric N(k)-paracontact metric manifolds. J. Math., 1–6 (2015)
Satō, I.: On a structure similar to the almost contact structure. Tensor (N.S.) 30, 219–224 (1976)
Sharma, R.: A 3-dimensional Sasakian metric as a Yamabe soliton. Int. J. Geom. Methods Mod. Phys. 9, 1220003 (2012)
Suh, Y.J., De, U.C.: Yamabe solitons and Ricci solitons on almost co-Kähler manifolds. Can. Math. Bull. 62(3), 653–661 (2019)
Suh, Y.J., Mondal, K.: Yamabe solitons on three-dimensional N(k)-paracontact metric manifolds. Bull. Iran. Math. Soc., 183–191 (2018)
Wang, Y.: Yamabe solitons on three dimensional Kenmotsu manifolds. Bull. Belg. Math. Soc. 23, 345–355 (2016)
Yamabe, H.: On a deformation of Riemannian structures on compact manifolds. Osaka Math. J. 12, 21–37 (1960)
Yano, K.: Integral Formulas in Riemannian geometry, Pure and Applied Mathematics, 1. Marcel Dekker, New York (1970)
Zamkovoy, S., Tzanov, V.: Non-existence of at paracontact metric structures in dimension greater than or equal to five. Annuaire Univ. Sofia Fac. Math. Inform. 100, 27–34 (2011)
Acknowledgements
The authors express their sincere gratitude to the anonymous referees for providing valuable suggestions in the improvement of the paper.
Funding
Not applicable.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Data availability
Not applicable.
Code availability
Not applicable.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
De, K., De, U.C. \(\delta \)-Almost Yamabe Solitons in Paracontact Metric Manifolds. Mediterr. J. Math. 18, 218 (2021). https://doi.org/10.1007/s00009-021-01856-9
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00009-021-01856-9