@Article{JMS-52-2,
author = {Zhuhong, Zhang},
title = {On the Triviality of a Certain Kind of Shrinking Solitons},
journal = {Journal of Mathematical Study},
year = {2019},
volume = {52},
number = {2},
pages = {169--177},
abstract = {<p style="text-align: justify;">In this paper, we study shrinking gradient Ricci solitons whose Ricci tensor
has one eigenvalue of multiplicity at least $n−2.$ Firstly, we show that if the minimal
eigenvalue of Ricci tensor has multiplicity at least $n−1$ at each point, then the soliton
are Einstein. While on the shrinking gradient Ricci solitons whose maximal eigenvalue
has multiplicity at least $n−1,$ the triviality are also true if we naturally require the
positivity of Ricci tensor.<br/>We further prove that if the maximal (or minimal) eigenvalue of Ricci tensor has multiplicity at least $n−2$ at each point , and in addition the sectional curvature is bounded
from above, then the soliton are Einstein.</p>},
issn = {2617-8702},
doi = {https://doi.org/10.4208/jms.v52n2.19.04},
url = {https://global-sci.com/article/87722/on-the-triviality-of-a-certain-kind-of-shrinking-solitons}
}