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**Isometry groups of Riemannian solvmanifolds.**
*(English)*
Zbl 0664.53022

A Riemannian solvmanifold is a connected Riemannian manifold M whose isometry group I(M) contains a transitive solvable Lie subgroup. The author constructs a single conjugacy class of almost simply transitive solvable subgroups of I(M) called the subgroups in standard position. Let M be a simply connected solvable Lie group R equipped with a left- invariant Riemannian metric. An algorithm for modifying R into a subgroup S of I(M) in standard position is constructed. If R is unimodular, then S is normal in I(M) which permits to describe the group I(M). The results are used for determining when two given Riemannian solvmanifolds are isometric. For a class of solvmanifolds M, all connected transitive subgroups of I(M) are described.

Reviewer: A.L.Onishchik

### MSC:

53C30 | Differential geometry of homogeneous manifolds |

### Keywords:

simply transitive group; Riemannian solvmanifold; isometry group; subgroups in standard position; solvable Lie group
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\textit{C. S. Gordon} and \textit{E. N. Wilson}, Trans. Am. Math. Soc. 307, No. 1, 245--269 (1988; Zbl 0664.53022)

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### References:

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