Isometric actions on pseudo-Riemannian nilmanifolds

Viviana del Barco; Gabriela P. Ovando

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arXiv · 1303.4450

Isometric actions on pseudo-Riemannian nilmanifolds

Viviana del Barco·Gabriela P. Ovando

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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 Riemannain 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 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 groups.

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BibTeX RIS

Viviana del Barco, Gabriela P. Ovando. 2013-03-18. Isometric actions on pseudo-Riemannian nilmanifolds. https://arxiv.org/abs/1303.4450

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