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


53C30 Differential geometry of homogeneous manifolds
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