Filiform nilsolitons of dimension 8

Details Filiform nilsolitons of dimension 8 Filiform nilsolitons of dimension 8

2008-10-24

arxiv.org/abs/0810.4530v1

Mathematics

Differential Geometry

12 pages, 2 tables

Scientific paper

A Riemannian manifold (M,g) is said to be Einstein if its Ricci tensor satisfies ric(g) = cg, for some real number c. In the homogeneous case, a problem that is still open is the so called Alekseevskii Conjecture. This conjecture says that any homogeneous Einstein space with negative scalar curvature (i.e. c < 0) is a solvmanifold: a simply connected solvable Lie group endowed with a left invariant Riemannian metric. The aim of this paper is to classify Einstein solvmanifolds of dimension 9 whose nilradicals are 7-step nilpotent Lie algebras of dimension 8.

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