Isometric actions on pseudo-Riemannian nilmanifolds

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.

18 pages

References in corpus (4)

• Lorentzian symmetric spaces in supergravity
• PseudoH-type 2-step nilpotent Lie groups
• Lattices and Periodic Geodesics in Pseudoriemannian 2-step Nilpotent Lie Groups
• Naturally reductive pseudo-Riemannian Lie groups in low dimensions