@article{Turki2024, 
author = {Nasser Bin Turki and Sharief Deshmukh},
title = {Sufficient conditions for triviality of Ricci solitons},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {1},
pages = {1346-1357},
keywords = {Ricci soliton, potential field, geodesic vector field, concurrent vector field},
url = {https://www.sciopen.com/article/10.3934/math.2024066},
doi = {10.3934/math.2024066},
abstract = {We found conditions on an    n-dimensional Ricci soliton        (          M      ,      g      ,              u            ,      λ        )   to be trivial. First, we showed that under an appropriate upper bound on the squared length of the covariant derivative of the potential field        u  , the Ricci soliton        (          M      ,      g      ,              u            ,      λ        )   reduces to a trivial soliton. We also showed that appropriate upper and lower bounds on the Ricci curvature    R  i  c      (                  u            ,              u              )   of a compact Ricci soliton        (          M      ,      g      ,              u            ,      λ        )   with potential field        u   geodesic vector field makes it a trivial soliton. We showed that if the Ricci operator    S of the Ricci soliton        (          M      ,      g      ,              u            ,      λ        )   is invariant under the potential field        u  , then        (          M      ,      g      ,              u            ,      λ        )   is trivial and the converse is also true. Finally, it was shown that if the potential field        u   of a connected Ricci soliton        (          M      ,      g      ,              u            ,      λ        )   is a concurrent vector field, then the Ricci soliton is shrinking.}
}