Ricci Solitons on Lorentzian Manifolds with Large Isometry Groups

Mathematics – Differential Geometry

Scientific paper

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Scientific paper

We show that Lorentzian manifolds whose isometry group is of dimension at
least $\frac{1}{2}n(n-1)+1$ are expanding, steady and shrinking Ricci solitons
and steady gradient Ricci solitons. This provides examples of complete locally
conformally flat and symmetric Lorentzian Ricci solitons which are not rigid.

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