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Article Dans Une Revue Differential Geometry and its Applications Année : 2018

Isometries of almost-Riemannian structures on Lie groups

Résumé

A simple Almost-Riemannian Structure on a Lie group G is defined by a linear vector field (that is an infinitesimal automorphism) and dim(G) − 1 left-invariant ones. It is first proven that two different ARSs are isometric if and only if there exists an isometry between them that fixes the identity. Such an isometry preserves the left-invariant distribution and the linear field. If the Lie group is nilpotent it is an automorphism. These results are used to state a complete classification of the ARSs on the 2D affine and the Heisenberg groups.
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Dates et versions

hal-01532085 , version 1 (02-06-2017)

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Philippe Jouan, Zsigmond † Guilherme, Victor Ayala. Isometries of almost-Riemannian structures on Lie groups. Differential Geometry and its Applications, 2018, ⟨10.1016/j.difgeo.2018.08.003⟩. ⟨hal-01532085⟩
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