On rotationally invariant shrinking gradient Ricci solitons

Details On rotationally invariant shrinking gradient Ricci solitons On rotationally invariant shrinking gradient Ricci solitons

2007-02-20

arxiv.org/abs/math/0702597v1

Mathematics

Differential Geometry

14 pages

Scientific paper

In this paper we study the gradient Ricci shrinking soliton equation on
rotationally symmetric manifolds of dimension three and higher and prove that
the only complete examples of such metrics on $S^n$, $\R{n}$ and $\R{}\times
S^{n-1}$ are, respectively, the round, flat, and standard cylindrical metrics.

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