Parabolic subgroups of semisimple Lie groups and Einstein solvmanifolds
Parabolic subgroups of semisimple Lie groups and Einstein solvmanifolds
复制标题
DOI：
10.1007/s00208-010-0589-0
复制
发表时间：
2007-11
影响因子：
1.4
通讯作者：
H. Tamaru
中科院分区：
文献类型：
--
作者：
H. Tamaru
本文研究了由任意半单李代数的任意抛物子代数构造的可解流形。这些溶剂流形是非紧型对称空间的齐次流形。我们证明了我们的溶剂流形的Ricci曲率与周围对称空间的Ricci曲率的限制重合。因此，我们所有的解流形都是爱因斯坦流形，这为非紧齐次爱因斯坦流形提供了大量的新例子。我们也证明了我们的解流形是最小的，但不是对称空间的完全测地线子流形。
In this paper, we study the solvmanifolds constructed from any parabolic subalgebras of any semisimple Lie algebras. These solvmanifolds are naturally homogeneous submanifolds of symmetric spaces of noncompact type. We show that the Ricci curvatures of our solvmanifolds coincide with the restrictions of the Ricci curvatures of the ambient symmetric spaces. Consequently, all of our solvmanifolds are Einstein, which provide a large number of new examples of noncompact homogeneous Einstein manifolds. We also show that our solvmanifolds are minimal, but not totally geodesic submanifolds of symmetric spaces.