Isometries of Almost-Riemannian Structures on Non-nilpotent, Solvable 3D Lie Groups

Víctor Ayala, Adriano Da Silva () and Danilo A. García Hernández
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Víctor Ayala: Instituto de Alta Investigación, Universidad de Tarapacá
Adriano Da Silva: Universidad de Tarapacá
Danilo A. García Hernández: Universidade Estadual de Campinas

Journal of Optimization Theory and Applications, 2025, vol. 207, issue 1, No 6, 31 pages

Abstract: Abstract In this paper, we show that automorphisms are the only isometries between rank-two almost-Riemannian structures on non-nilpotent, solvable, connected 3D Lie groups. As a consequence, we obtain a classification of rank-two almost-Riemannian structures on these groups.

Keywords: Almost-Riemannian geometry; solvable lie groups; isometry; 22E15; 22E25; 53C17; 53C15 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02768-4

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