K-Cosymplectic manifolds

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• 作者：Giovanni Bazzoni ; Oliver Goertsches
• 关键词：K ; Cosymplectic ; Basic cohomology ; Momentum map ; Deformations ; Closed Reeb orbit ; Primary 53C25 ; 53D15 ; Secondary 53C12 ; 53D20 ; 55N91
• 刊名：Annals of Global Analysis and Geometry
• 出版年：2015
• 出版时间：March 2015
• 年：2015
• 卷：47
• 期：3
• 页码：239-270
• 全文大小：373 KB
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• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Analysis
  Statistics for Business, Economics, Mathematical Finance and Insurance
  Mathematical and Computational Physics
  Group Theory and Generalizations
  Geometry
  
• 出版者：Springer Netherlands
• ISSN：1572-9060

文摘

In this paper we study K-cosymplectic manifolds, i.e., smooth cosymplectic manifolds for which the Reeb field is Killing with respect to some Riemannian metric. These structures generalize coK?hler structures, in the same way as K-contact structures generalize Sasakian structures. In analogy to the contact case, we distinguish between (quasi-)regular and irregular structures; in the regular case, the K-cosymplectic manifold turns out to be a flat circle bundle over an almost K?hler manifold. We investigate de Rham and basic cohomology of K-cosymplectic manifolds, as well as cosymplectic and Hamiltonian vector fields and group actions on such manifolds. The deformations of type I and II in the contact setting have natural analogues for cosymplectic manifolds; those of type I can be used to show that compact K-cosymplectic manifolds always carry quasi-regular structures. We consider Hamiltonian group actions and use the momentum map to study the equivariant cohomology of the canonical torus action on a compact K-cosymplectic manifold, resulting in relations between the basic cohomology of the characteristic foliation and the number of closed Reeb orbits on an irregular K-cosymplectic manifold.