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

Víctor Ayala; Adriano Da Silva; Danilo A.García Hernández

doi:10.1007/s10957-025-02768-4

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

Víctor Ayala
, Adriano Da Silva
, Danilo A.García Hernández

Universidade Estadual de Campinas

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Article number	6
Journal	Journal of Optimization Theory and Applications
Volume	207
Issue number	1
DOIs	https://doi.org/10.1007/s10957-025-02768-4
State	Published - Oct 2025

Keywords

Almost-Riemannian geometry
isometry
solvable lie groups

Access to Document

10.1007/s10957-025-02768-4

Cite this

@article{ade2f9ee68bd4a85b88d634df4ae3719,

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

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, isometry, solvable lie groups",

author = "V{\'i}ctor Ayala and Silva, \{Adriano Da\} and Hern{\'a}ndez, \{Danilo A.Garc{\'i}a\}",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.",

year = "2025",

month = oct,

doi = "10.1007/s10957-025-02768-4",

language = "English",

volume = "207",

journal = "Journal of Optimization Theory and Applications",

issn = "0022-3239",

number = "1",

}

TY - JOUR

T1 - Isometries of Almost-Riemannian Structures on Non-nilpotent, Solvable 3D Lie Groups

AU - Ayala, Víctor

AU - Silva, Adriano Da

AU - Hernández, Danilo A.García

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.

PY - 2025/10

Y1 - 2025/10

N2 - 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.

AB - 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.

KW - Almost-Riemannian geometry

KW - isometry

KW - solvable lie groups

UR - https://www.scopus.com/pages/publications/105009966566

U2 - 10.1007/s10957-025-02768-4

DO - 10.1007/s10957-025-02768-4

M3 - Article

AN - SCOPUS:105009966566

SN - 0022-3239

VL - 207

JO - Journal of Optimization Theory and Applications

JF - Journal of Optimization Theory and Applications

IS - 1

M1 - 6

ER -

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

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this