English

Souriau-Fisher metric and Completely integrable system on Lie groups SO(2) and SO(3)

Differential Geometry 2026-01-23 v4

Abstract

We study the generalize Fisher metric on SO(2) and SO(3) via the thermodynamics Lie group theories of Souriau. Then we give the effect of 2-cocycle on the integrability of gradient systems due to the Fisher metric and Souriau-Fisher metric. In addition, we show how the cocycle can locally modify the Fisher metric on a coadjoint orbit, in explicit terms of brackets and central extensions on the Lie groups SO(2) and SO(3).

Keywords

Cite

@article{arxiv.2509.20910,
  title  = {Souriau-Fisher metric and Completely integrable system on Lie groups SO(2) and SO(3)},
  author = {Prosper Rosaire Mama Assandje and Michel Bertrand Djiadeu Ngaha and Romain Nimpa Pefoukeu and Salomon Joseph Mbatakou},
  journal= {arXiv preprint arXiv:2509.20910},
  year   = {2026}
}