Complete gradient shrinking Ricci solitons with pinched curvature

Details Complete gradient shrinking Ricci solitons with pinched curvature Complete gradient shrinking Ricci solitons with pinched curvature

2011-03-31

arxiv.org/abs/1104.0023v4

Mathematics

Differential Geometry

Scientific paper

We prove that any $n$--dimensional complete gradient Ricci soliton with
pinched Weyl curvature is a finite quotient of $\RR^{n}$, $\RR \times
\SS^{n-1}$ or $\SS^{n}$. In particular, we do not need to assume the metric to
be locally conformally flat.

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