Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 14 (2019), 231 -- 259

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RÉALISATION DU FLOT GÉODÉSIQUE SUR LE GROUPE SO(n) COMME FLOT SUR DES ORBITES DE KOTANT-KIRILLOV/REALIZATION OF GEODESIC FLOW ON THE GROUP SO(n) AS A FLOW ON KOSTANT-KIRILLOV ORBITS

Ahmed Lesfari

Abstract. The aim of this paper is to realize the geodesic flow on the group SO(n) as a flow on the Kostant-Kirillov orbits. We study the adjoint and coadjoint orbits of a Lie group with an application in the case of the orthogonal special group SO(n). We will see how to explicitly determine a symplectic structure in the orbit of the coadjoint representation of a Lie group. Special attention is given to the groups SO(3) and SO(4).

2010 Mathematics Subject Classification: 53D05; 53D30.
Keywords: Symplectic manifolds; Symplectic structures.

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Ahmed Lesfari
Département de Mathématiques,
Faculté des Sciences, Université Chouaïb Doukkali,
B.P. 20, 24000 El Jadida, Maroc.
e-mail: lesfariahmed@yahoo.fr

http://www.utgjiu.ro/math/sma