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\"ahler 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\"ahler 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.

K-cosymplectic manifolds

Bazzoni G;
2015

Abstract

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\"ahler 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\"ahler 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.
http://link.springer.com/article/10.1007/s10455-014-9444-y
K-cosymplectic; basic cohomology; momentum map
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11383/2086814
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