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- W4297210321 abstract "In this paper we consider a perturbation of the Ricci solitons equation proposed by J. P. Bourguignon in cite{jpb1}. We show that these structures are more rigid then standard Ricci solitons. In particular, we prove that there is only one complete three--dimensional, positively curved, Riemannian manifold satisfying $$ Ric -frac{1}{2} R , g , + , nabla^2 f , = ,0,, $$ for some smooth function $f$. This solution is rotationally symmetric and asymptotically cylindrical and it represents the analogue of the Hamilton's cigar in dimension three. The key ingredient in the proof is the rectifiability of the potential function $f$. It turns out that this property holds also in the Lorentzian setting and for a more general class of structures which includes some gravitational theories." @default.
- W4297210321 created "2022-09-27" @default.
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- W4297210321 date "2012-01-31" @default.
- W4297210321 modified "2023-09-23" @default.
- W4297210321 title "Gradient Einstein solitons" @default.
- W4297210321 doi "https://doi.org/10.48550/arxiv.1201.6620" @default.
- W4297210321 hasPublicationYear "2012" @default.
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