Noncompact homogeneous Einstein manifolds attached to graded Lie algebras
Noncompact homogeneous Einstein manifolds attached to graded Lie algebras
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DOI：
10.1007/s00209-007-0217-1
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发表时间：
2006-10
影响因子：
0.8
通讯作者：
H. Tamaru
中科院分区：
文献类型：
--
作者：
H. Tamaru
在本文中，我们研究半单李代数的抛物型子代数的零根及其自然一维可解推广。我们研究相关尼尔流形和求解流形的结构、曲率和爱因斯坦条件。我们证明，如果零根是两步的，那么我们的求解流形就是爱因斯坦。还给出了具有三步和四步零自由基的爱因斯坦求解流形的新例子。
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 two-step. New examples of Einstein solvmanifolds with three-step and four-step nilradicals are also given.