Some Results of Ricci Bi-Conformal Vector Fields

Document Type : Original Scientific Paper

Authors

Department of Pure Mathematics, ‎Faculty of Science,‎ ‎Imam Khomeini International University, ‎Qazvin‎, ‎I‎. ‎R‎. ‎Iran

10.22052/mir.2025.256100.1494

Abstract

‎The investigation of Ricci bi-conformal vector fields and their associated outcomes is crucial for gaining insights into the geometric and topological characteristics of the underlying manifolds‎. ‎The study of conformal vector fields and their extensions is highly valuable in the realms of geometry and physics‎. ‎In this manuscript‎, ‎we study the topological properties of the Ricci bi-conformal vector field‎. ‎The goal of this paper is to find some results of the Ricci bi-conformal vector fields‎. ‎We prove that a complete manifold admits the Ricci bi-conformal vector fields has a finite fundamental group‎. ‎For this purpose‎, ‎we first state the definition and lemma‎, ‎and then use them to prove our theorems‎.

Keywords

References

[1] U. C. De, A. Sardar and A. Sarkar, Some conformal vector fields and conformal Ricci solitons on N(k)-contact metric manifolds, AUT J. Math. Comput. 2 (2021) 61 - 71, https://doi.org/10.22060/ajmc.2021.19220.1043.
[2] M. Sohrabpour and S. Azami, Ricci solitons and Ricci bi-conformal vector fields on the model space Sol4
1, Honam Math. J. 46 (2024) 393 - 406, https://doi.org/10.5831/HMJ.2024.46.3.393.
[3] M. Sohrabpour and S. Azami, Ricci bi-conformal vector fields on Lorentzian Walker manifolds of low dimension, Lobachevskii J. Math. 44 (2023) 5437 -5443, https://doi.org/10.1134/S1995080223120338.
[4] M. Anastasiei, A generalization of Myers theorem, An. Stiinµ. Univ. Al. I. Cuza Iasi. Mat. (N.S.) (2007) 33 - 40.
[5] S. Azami, Complete Ricci-bourguignon solitons on Finsler manifolds, J. Finsler Geom. Appl. 2 (2021) 108 - 117,
https://doi.org/10.22098/jfga.2021.1268.
[6] S. Azami, Complete shrinking general Ricci flow soliton systems, Math. Notes 114 (2023) 675 - 678, https://doi.org/10.1134/S0001434623110044.
[7] S. Azami, V. Pirhadi and G. Fasihi-Ramandi, Complete shrinking Riccibourguignon harmonic solitons, Internat. J. Math. 33 (2022) #2250046.
[8] W. Wylie, Complete shrinking Ricci solitons have finite fundamental group, Proc. Amer. Math. Soc. 136 (2008) 1803 - 1806.
Mathematics Interdisciplinary Research
Volume 10, Issue 3
In progress
September 2025
Pages 245-250

Files

Share

How to cite

Statistics