ON HOMOGENEOUS RICCI SOLITONS
By Ramiro A. Lafuente, Jorge Lauret. 2012
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We study the evolution of homogeneous Ricci solitons under the bracket flow, a dynamical system on the space of all homogeneous spaces of dimension n with a q-dimensional isotropy, which is equivalent to the Ricci flow for homogeneous manifolds. We prove that algebraic solitons (i.e. the Ricci operator is a multiple of the identity plus a derivation) are precisely the fixed points of the system, and that a homogeneous Ricci soliton is isometric to an algebraic soliton if and only if the corresponding bracket flow solution is not chaotic, in the sense that its omega-limit set consists of a single point. We also geometrically characterize algebraic solitons among homogeneous Ricci solitons as those for which the Ricci flow solution is simultaneously diagonalizable.
Subfields: Algebra and Number Theory
View Paper: https://www.semanticscholar.org/paper/87f806724fe834139668d87b1394ed77aafaed43
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In Algebra and Number Theory
Citations in the corpus
- Immortal homogeneous Ricci flows (2017, background): “erivative of gin the direction of a smooth vector field Xon Mn. For expanding homogeneous Ricci solitons there exists already a well-developed structure theory: see [Heb98], [Lau10], [Nik11], [Jab14], [LL14a], [LL14b], [Jab15], [HPW15], [GJ17], [JP16], [AL17]. By [PW09], these solitons are either the”
- Homogeneous Ricci Solitons are Algebraic (2013, background): “(This follows from [7] together with [11] by Lafuente and Lauret.”
- Laplacian Flow of Closed G$$_2$$2-Structures Inducing Nilsolitons (2013, unknown): “Formore details, see for instance [7,17,19].”