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

Prosper Rosaire Mama Assandje; Michel Bertrand Djiadeu Ngaha; Romain Nimpa Pefoukeu; Salomon Joseph Mbatakou

paper

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

arXiv:2509.20910

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).