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arXiv · 2509.20910

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
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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).

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Prosper Rosaire Mama Assandje, Michel Bertrand Djiadeu Ngaha, Romain Nimpa Pefoukeu, Salomon Joseph Mbatakou. 2025-09-25. Souriau-Fisher metric and Completely integrable system on Lie groups SO(2) and SO(3). https://arxiv.org/abs/2509.20910

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