Einstein solvmanifolds are standard

• 成果类型: Article
• 署名作者: Lauret, Jorge
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2010.172.1859
• 发表日期: 2010
• 页码: 1859-1877
• 关键词: moment map; instability; CURVATURE; MANIFOLDS; SPACES

摘要

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 shown that under a simple algebraic condition (he calls such a solvmanifold standard), 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 adapted from one in geometric invariant theory due to F. Kirwan.