arXiv Analytics

Sign in

arXiv:math/0610675 [math.DG]AbstractReferencesReviewsResources

Noncompact homogeneous Einstein manifolds attached to graded Lie algebras

Hiroshi Tamaru

Published 2006-10-23Version 1

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.

Comments: 19 pages, the first version was written in March 2004
Categories: math.DG
Subjects: 53C30, 22E25, 53C25, 53C35
Related articles: Most relevant | Search more
arXiv:2305.02378 [math.DG] (Published 2023-05-03)
The mean curvature flow on solvmanifolds
arXiv:1709.09126 [math.DG] (Published 2017-09-26)
Stratified hyperkahler spaces from semisimple Lie algebras
arXiv:2007.14541 [math.DG] (Published 2020-07-29)
Deformations of Adjoint orbits for semisimple Lie algebras and Lagrangian submanifolds

Links

Toolbox