Einstein Solvmanifolds Are Standard

نویسنده

  • JORGE LAURET
چکیده

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 [H] has showed that under certain simple algebraic condition (such a solvmanifold is called 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 from geometric invariant theory due to F. Kirwan [K].

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تاریخ انتشار 2007