Rank-one Einstein solvmanifolds of dimension 7

被引：50

作者：

Will, C

机构：

[1] Univ Nacl Cordoba, FaMAF, RA-5000 Cordoba, Argentina

[2] Univ Nacl Cordoba, CIEM, RA-5000 Cordoba, Argentina

来源：

DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS | 2003年 / 19卷 / 03期

关键词：

Einstein; solvmanifold; critical points; nilpotent and solvable Lie groups; left invariant metrics;

D O I：

10.1016/S0926-2245(03)00037-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We use a variational approach to determine explicitly all the 7-dimensional rank-one Einstein solvmanifolds. We prove that each one of the 34 nilpotent Lie algebras of dimension 6 admits a rank-one solvable extension which can be endowed with an Einstein left-invariant Riemannian metric. This also produces 34 Ricci soliton metrics on R-6 which are homogeneous. (C) 2003 Elsevier B.V. All rights reserved.

引用

页码：307 / 318

页数：12

共 12 条

[1]

Alekseevskii D., 1971, MAT SBORNIK, V84, P14

[2]

BESSE A, 1987, ERGEB MATH, V10

[3] Alekseevskian spaces [J].