English

Noncompact homogeneous Einstein manifolds attached to graded Lie algebras

Differential Geometry 2007-05-23 v1

Abstract

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.

Keywords

Cite

@article{arxiv.math/0610675,
  title  = {Noncompact homogeneous Einstein manifolds attached to graded Lie algebras},
  author = {Hiroshi Tamaru},
  journal= {arXiv preprint arXiv:math/0610675},
  year   = {2007}
}

Comments

19 pages, the first version was written in March 2004