Einstein solvmanifolds and nilsolitons

By Jorge Lauret. 2008

88 citations recorded by the source corpus.

The purpose of the present expository paper is to give an account of the recent progress and present status of the classification of solvable Lie groups admitting an Einstein left invariant Riemannian metric, the only known examples so far of noncompact Einstein homogeneous manifolds. The problem turns to be equivalent to the classification of Ricci soliton left invariant metrics on nilpotent Lie groups.

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

View Paper: https://www.semanticscholar.org/paper/5ac70d6411ca3d213d8b0f1d517375612422d842

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In Applied Mathematics

In Astronomy and Astrophysics

In Geometry and Topology

Citations in the corpus

The Ricci flow for simply connected nilmanifolds (2010, background): “Nilsolitons have been extensively studied because of their interplay with Einstein solvmanifolds (see the survey [21]).”
Laplacian Flow of Closed G$$_2$$2-Structures Inducing Nilsolitons (2013, background): “Recently, Lauret in [20,21] proved the following”
Structure of homogeneous Ricci solitons and the Alekseevskii conjecture (2012, background): “In the homogeneous case, the Einstein equation becomes a subtle system of algebraic equations, and the following main general question is still open in both, the compact and noncompact cases: Which homogeneous spaces G/K admit a G-invariant Einstein Riemannian metric? We refer to the surveys [30, 22”