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- W4301751941 abstract "We prove that the Ricci flow g(t) starting at any metric on the euclidean space that is invariant by a transitive nilpotent Lie group N, can be obtained by solving an ODE for a curve of nilpotent Lie brackets. By using that this ODE is the negative gradient flow of a homogeneous polynomial, we obtain that g(t) is type-III, and, up to pull-back by time-dependent diffeomorphisms, that g(t) converges to the flat metric, and the rescaling |R(g(t))|g(t) converges smoothly to a Ricci soliton, uniformly on compact sets. The Ricci soliton limit is also invariant by some transitive nilpotent Lie group, though possibly non-isomorphic to N." @default.
- W4301751941 created "2022-10-05" @default.
- W4301751941 creator A5020454082 @default.
- W4301751941 date "2010-04-06" @default.
- W4301751941 modified "2023-09-23" @default.
- W4301751941 title "The Ricci flow for simply connected nilmanifolds" @default.
- W4301751941 doi "https://doi.org/10.48550/arxiv.1004.0946" @default.
- W4301751941 hasPublicationYear "2010" @default.
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