Homogeneous Ricci solitons
By Michael Jablonski. 2011
46 citations recorded by the source corpus.
In this work, we study metrics which are both homogeneous and Ricci soliton. If there exists a transitive solvable group of isometries on a Ricci soliton, we show that it is isometric to a solvsoliton. Moreover, unless the manifold is flat, it is necessarily simply-connected and diffeomorphic to $\mathbb R^n$. In the general case, we prove that homogeneous Ricci solitons must be semi-algebraic Ricci solitons in the sense that they evolve under the Ricci flow by dilation and pullback by automorphisms of the isometry group. In the special case that there exists a transitive semi-simple group of isometries on a Ricci soliton, we show that such a space is in fact Einstein. In the compact case, we produce new proof that Ricci solitons are necessarily Einstein. Lastly, we characterize solvable Lie groups which admit Ricci soliton metrics.
Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/9fa425b103ae1b82ab94d485ebda013f15c55035
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In Applied Mathematics
In Astronomy and Astrophysics
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Citations in the corpus
- Examples of Algebraic Ricci Solitons in the Pseudo-Riemannian Case (2011, background): “ei,ej). It is naturalto considerthe opposite ofTheorem2.5. A Riemannianmanifold (M,g) is called a solvmanifold if there exists a transitive solvable group of isometries. Jablonski proved Theorem 2.6 ([12]). Consider a solvmanifold (M,g) which is a Ricci soliton. Then (M,g) is isometric to a solvsoli”
- Algebraic Ricci Solitons of three-dimensional Lorentzian Lie groups (2011, background): “γ= 0. It is naturalto considerthe opposite ofTheorem1.1. A Riemannianmanifold (M,g) is called a solvmanifold if there exists a transitive solvable group of isometries. Jablonski proved 3 Theorem 1.3 ([15]). Consider a solvmanifold (M,g) which is a Ricci soliton. Then (M,g) is isometric to a solvsoli”