Year: 2019
Author: Zhuhong Zhang
Journal of Mathematical Study, Vol. 52 (2019), Iss. 2 : pp. 169–177
Abstract
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.
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v52n2.19.04
Journal of Mathematical Study, Vol. 52 (2019), Iss. 2 : pp. 169–177
Published online: 2019-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 9
Keywords: Einstein manifold shrinking gradient Ricci soliton positive Ricci curvature pinched sectional curvature.