Einstein solvmanifolds are standard

Details Einstein solvmanifolds are standard Einstein solvmanifolds are standard

2007-03-15

arxiv.org/abs/math/0703472v2

Mathematics

Differential Geometry

15 pages, final version to appear in Ann. of Math

Scientific paper

We study Einstein manifolds admitting a transitive solvable Lie group of isometries (solvmanifolds). It is conjectured that these exhaust the class of noncompact homogeneous Einstein manifolds. J. Heber has showed that under certain simple algebraic condition called standard (i.e. the orthogonal complement of the derived algebra is abelian), Einstein solvmanifolds have many remarkable structural and uniqueness properties. In this paper, we prove that any Einstein solvmanifold is standard, by applying a stratification procedure from geometric invariant theory due to F. Kirwan.

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