Isometric actions on pseudo-Riemannian nilmanifolds |
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Authors: | Viviana del Barco Gabriela P Ovando |
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Institution: | 1. ECEN-FCEIA, Universidad Nacional de Rosario, Pellegrini 250, 2000, Rosario, Argentina 2. ECEN-FCEIA, CONICET, Universidad Nacional de Rosario, Pellegrini 250, 2000, Rosario, Argentina
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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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