Details
| Originalsprache | Englisch |
|---|---|
| Aufsatznummer | rnaf002 |
| Fachzeitschrift | International Mathematics Research Notices |
| Jahrgang | 2025 |
| Ausgabenummer | 3 |
| Frühes Online-Datum | 29 Jan. 2025 |
| Publikationsstatus | Veröffentlicht - Feb. 2025 |
Abstract
Four subriemannian (SR) structures over the Euclidean sphere are considered in accordance to the previous literature. The defining bracket generating distribution is chosen as the horizontal space in the Hopf fibration, the quaternionic Hopf fibration, or spanned by a suitable number of canonical vector fields. In all cases the induced SR geodesic flow on is studied. Adapting a method by A. Thimm in [36], a maximal set of functionally independent and Poisson commuting first integrals are constructed, including the corresponding SR Hamiltonian. As a result, the complete integrability in the sense of Liouville is proved for the SR geodesic flow. It is observed that these first integrals arise as the symbols of commuting second-order differential operators one of them being a (not necessarily intrinsic) sublaplacian. On the way one explicitly derives the Lie algebras of all SR isometry groups intersected with.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Allgemeine Mathematik
Zitieren
- Standard
- Harvard
- Apa
- Vancouver
- BibTex
- RIS
in: International Mathematics Research Notices, Jahrgang 2025, Nr. 3, rnaf002, 02.2025.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Complete Integrability of Subriemannian Geodesic Flows on S7
AU - Bauer, Wolfram
AU - Laaroussi, Abdellah
AU - Tarama, Daisuke
N1 - Publisher Copyright: © 2025 The Author(s).
PY - 2025/2
Y1 - 2025/2
N2 - Four subriemannian (SR) structures over the Euclidean sphere are considered in accordance to the previous literature. The defining bracket generating distribution is chosen as the horizontal space in the Hopf fibration, the quaternionic Hopf fibration, or spanned by a suitable number of canonical vector fields. In all cases the induced SR geodesic flow on is studied. Adapting a method by A. Thimm in [36], a maximal set of functionally independent and Poisson commuting first integrals are constructed, including the corresponding SR Hamiltonian. As a result, the complete integrability in the sense of Liouville is proved for the SR geodesic flow. It is observed that these first integrals arise as the symbols of commuting second-order differential operators one of them being a (not necessarily intrinsic) sublaplacian. On the way one explicitly derives the Lie algebras of all SR isometry groups intersected with.
AB - Four subriemannian (SR) structures over the Euclidean sphere are considered in accordance to the previous literature. The defining bracket generating distribution is chosen as the horizontal space in the Hopf fibration, the quaternionic Hopf fibration, or spanned by a suitable number of canonical vector fields. In all cases the induced SR geodesic flow on is studied. Adapting a method by A. Thimm in [36], a maximal set of functionally independent and Poisson commuting first integrals are constructed, including the corresponding SR Hamiltonian. As a result, the complete integrability in the sense of Liouville is proved for the SR geodesic flow. It is observed that these first integrals arise as the symbols of commuting second-order differential operators one of them being a (not necessarily intrinsic) sublaplacian. On the way one explicitly derives the Lie algebras of all SR isometry groups intersected with.
UR - http://www.scopus.com/inward/record.url?scp=85216708674&partnerID=8YFLogxK
U2 - 10.1093/imrn/rnaf002
DO - 10.1093/imrn/rnaf002
M3 - Article
AN - SCOPUS:85216708674
VL - 2025
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
SN - 1073-7928
IS - 3
M1 - rnaf002
ER -