Abstract
This work deals with the structure of the isometry group of pseudo-Riemannian 2-step nilmanifolds. We study the action by isometries of several groups and we construct examples showing substantial differences with the Riemannian situation; for instance, the action of the nilradical of the isometry group does not need to be transitive. For a nilpotent Lie group endowed with a left-invariant pseudo-Riemannian metric, we study conditions for which the subgroup of isometries fixing the identity element equals the subgroup of isometric automorphisms. This set equality holds for pseudo-\(H\)-type Lie groups.
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Work partially supported by SCyT-UNR and ANPCyT grants. V. del Barco also supported by a CONICET fellowship.
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del Barco, V., Ovando, G.P. Isometric actions on pseudo-Riemannian nilmanifolds. Ann Glob Anal Geom 45, 95–110 (2014). https://doi.org/10.1007/s10455-013-9389-6
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DOI: https://doi.org/10.1007/s10455-013-9389-6