On Cosymplectic Dynamics I

Author:

Tchuiaga Stephane1,Houenou Franck2,Bikorimana Pierre3

Affiliation:

1. Department of Mathematics , University of Buea , Po.Box 63, Buea- Cameroon , Cameroon

2. Department of Mathematics , University of Abomey Calavi , Bénin

3. Institut de Mathématiques et de Sciences Physiques , University of Abomey Calavi , Po.box 613, Benin, Bénin

Abstract

Abstract This paper is an introduction to cosymplectic topology. Through it, we study the structures of the group of cosymplectic diffeomorphisms and the group of almost cosymplectic diffeomorphisms of a cosymplectic manifold (M, ω, η) : (i)− we define and present the features of the space of almost cosymplectic vector fields (resp. cosymplectic vector fields); (ii)− we prove by a direct method that the identity component in the group of all cosymplectic diffeomorphisms is C 0−closed in the group Diff (M) (a rigidity result), while in the almost cosymplectic case, we prove that the Reeb vector field determines the almost cosymplectic nature of the C 0−limit ϕ of a sequence of almost cosymplectic diffeomorphisms (a rigidity result). A sufficient condition based on Reeb’s vector field which guarantees that ϕ is a cosymplectic diffeomorphism is given (a ˛exibility condition), the cosymplectic analogues of the usual symplectic capacity-inequality theorem are derived and the cosymplectic analogue of a result that was proved by Hofer-Zehnder follows.

Publisher

Walter de Gruyter GmbH

Subject

Geometry and Topology

Cited by 3 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Revisiting the generalized virial theorem and its applications from the perspective of contact and cosymplectic geometry;International Journal of Geometric Methods in Modern Physics;2024-07-27

2. On Darboux theorems for geometric structures induced by closed forms;Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas;2024-06-20

3. Towards the cosymplectic topology;Complex Manifolds;2023-01-01

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