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Complete Integrability of Subriemannian Geodesic Flows on S7

Research output: Contribution to journalArticleResearchpeer review

Authors

  • Wolfram Bauer
  • Abdellah Laaroussi
  • Daisuke Tarama

Research Organisations

External Research Organisations

  • Ritsumeikan University

Details

Original languageEnglish
Article numberrnaf002
JournalInternational Mathematics Research Notices
Volume2025
Issue number3
Early online date29 Jan 2025
Publication statusPublished - 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 subject areas

Cite this

Complete Integrability of Subriemannian Geodesic Flows on S7. / Bauer, Wolfram; Laaroussi, Abdellah; Tarama, Daisuke.
In: International Mathematics Research Notices, Vol. 2025, No. 3, rnaf002, 02.2025.

Research output: Contribution to journalArticleResearchpeer review

Bauer W, Laaroussi A, Tarama D. Complete Integrability of Subriemannian Geodesic Flows on S7. International Mathematics Research Notices. 2025 Feb;2025(3):rnaf002. Epub 2025 Jan 29. doi: 10.1093/imrn/rnaf002
Bauer, Wolfram ; Laaroussi, Abdellah ; Tarama, Daisuke. / Complete Integrability of Subriemannian Geodesic Flows on S7. In: International Mathematics Research Notices. 2025 ; Vol. 2025, No. 3.
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