Noncompact homogeneous Einstein manifolds attached to graded Lie algebras

Details Noncompact homogeneous Einstein manifolds attached to graded Lie algebras Noncompact homogeneous Einstein manifolds attached to graded Lie algebras

2006-10-23

arxiv.org/abs/math/0610675v1

Mathematics

Differential Geometry

19 pages, the first version was written in March 2004

Scientific paper

In this paper, we study the nilradicals of parabolic subalgebras of semisimple Lie algebras and the natural one-dimensional solvable extensions of them. We investigate the structures, curvatures and Einstein conditions of the associated nilmanifolds and solvmanifolds. We show that our solvmanifold is Einstein if the nilradical is of two-step. New examples of Einstein solvmanifolds with three-step and four-step nilradicals are also given.

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