On a Normal Conformal Cosymplectic Manifold

Abstract

We deal with a normal conformal cosymplectic (2m+ 1)-dimensional manifold M(Ω, ∅, η. ξ, g), with Ω as the fundamental 2-form and η the Reeb covector field.

Following [1], there exists a unique vector field X ^λ such that

$$\Omega ({X_\lambda }) = i{x_\lambda }\Omega = d\lambda - \xi (\lambda )\eta $$

Xλ is called a Hamiltonian vector field. It is proved that Xλ defines a relative conformal transformation of Q. A necessary and sufficient condition that X ^λ be a skew symmetric Killing vector field with the Reeb vector field as generative is obtained. Finally, it is shown that X ^λ defines a contact transformation of its dual 1-form X^b _λ .