Ricci soliton homogeneous nilmanifolds

By Jorge Lauret. 2001

235 citations recorded by the source corpus.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/af4bd97d9a0b555ba077b64187077d7296920df9

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In Applied Mathematics

In Astronomy and Astrophysics

In Geometry and Topology

Citations in the corpus

On Ricci solitons of cohomogeneity one (2008, background): “ompact homogeneous Ricci solitons exist, and there is a beautiful correspondence between left-invariant Einstein metrics on solvable Lie groups and homogeneous Ricci solitons on their nilradicals (cf [La], [FDC]). Thenextstep upin complexity fromhomogeneous metrics arethose of cohomogeneity one, tha”
Some New Examples of Non-K\"ahler Ricci Solitons (2008, unknown): “, [ChV], [G], [PTV], [FIK], [PS] and [ACGT]. Most of the known examples of Ricci solitons are indeed Ka¨hler. The exceptions of which we are aware are the homogeneous solitons on nilpotent Lie groups [La], the rotationally symmetric Bryant solitons [Bry] on Rn (n > 2), Ivey’s generalization of th”
ON HOMOGENEOUS RICCI SOLITONS (2012, unknown): “ that they should not exist, but they do. Actually, the nilpotent part of any Einstein solvable Lie group gives an example of a homogeneous Ricci soliton, known as a nilsoliton in the literature (see [L01]). One may also extend a This research was partially supported by grants from CONICET, FONCYT a”
Homogeneous Ricci solitons (2011, methodology): “etrics. For example, while nilmanifolds are unable to admit Einstein metrics [Jen69], they often admit Ricci soliton metrics [Jab11b], Ricci solitons are measurably the closest one can be to Einstein [Lau01], and such metrics have maximal symmetry when they exist [Jab11a]. The classiﬁcation of homog”
Degenerations of Lie algebras and geometry of Lie groups (2003, methodology): “Several examples of critical nilpotent Lie algebras are given in [24] using these characterizations.”
Recent Progress on Ricci Solitons (2009, background): “Also, there exist complete noncompact Ricci solitons (steady, shrinking and expanding) that are not Einstein.”
Ricci soliton solvmanifolds (2010, background): “ (5) nicely combines the geometric and algebraic features of a leftinvariant metric on a Lie group, providing a neat way to ﬁnd examples of homogeneous Ricci solitons. These examples ﬁrst appeared in [L1] (G nilpotent), [BD] (G solvable, dimG = 3) and [IJL] (G solvable, dimG = 4). Remark 2.1. It is ”
Einstein solvmanifolds: existence and non-existence questions (2006, background): “We now describe some interplays found in [7,8,11] between standard Einstein solvmanifolds, critical points of moment maps and Ricci soliton metrics.”
The existence of soliton metrics for nilpotent Lie groups (2008, background): “Thus, we have shown that (n−�2µ1−�1µ2,Q) is a nilsoliton metric Lie algebra isomorphic to Qn. Uniqueness follows from [ Lau01a ].”
Examples of Algebraic Ricci Solitons in the Pseudo-Riemannian Case (2011, background): “If g is a solvsoliton, then g is Einstein (see [13]).”
Structure of homogeneous Ricci solitons and the Alekseevskii conjecture (2012, methodology): “Parts (i) and (ii) may be viewed as a generalization of the link between Einstein solvmanifolds and nilsolitons discovered in [20].”
Algebraic Ricci Solitons of three-dimensional Lorentzian Lie groups (2011, background): “In [16], Lauret studied the relation between algebraic Ricci solitons and Ricci solitons on Riemannian manifolds.”
RIGIDITY OF GRADIENT RICCI SOLITONS (2007, unknown): “For a suitable constant ↵ r 6 = r 1 . f 2 2 � f .”