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Abstract
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In this paper, we prove some classification theorems for gradient expanding and
steady Ricci solitons. We show that a complete noncompact radially Ricci flat (i.e.,
)
gradient expanding Ricci soliton with nonnegative Ricci curvature is a finite quotient
of
.
Moreover, we prove that a complete noncompact gradient expanding Ricci soliton with
and
is a finite
quotient of
.
For a nontrivial complete noncompact radially Ricci flat (i.e.,
) gradient steady
Ricci soliton with
for some
,
we show that it is Einstein with vanishing Ricci curvature or a quotient of
or of the
product
with
,
where
is Einstein with vanishing Ricci curvature.
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Keywords
gradient expanding Ricci soliton, gradient steady Ricci
soliton
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Mathematical Subject Classification 2010
Primary: 53C21, 53C25
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Milestones
Received: 21 July 2017
Revised: 13 August 2018
Accepted: 29 October 2018
Published: 16 September 2019
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