International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 2, Pages 267-278
doi:10.1155/S0161171296000373
On a class of exact locally conformal cosymlectic manifolds
1Department Wiskunde, Katholieke Universiteit Leuven, Celestijnenlaan 200 B, Leuven B – 3000, Belgium
259 Avenue Emile Zola, Paris 75015, France
Received 6 May 1993; Revised 1 June 1994
Copyright © 1996 I. Mihai et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
An almost cosymplectic manifold M is a (2m+1)-dimensional oriented Riemannian
manifold endowed with a 2-form Ω of rank 2m, a 1-form η such that Ωm Λ η≠0 and a vector field ξ
satisfying iξΩ=0 and η(ξ)=1. Particular cases were considered in [3] and [6].
Let (M,g) be an odd dimensional oriented Riemannian manifold carrying a globally defined vector
field T such that the Riemannian connection is parallel with respect to T. It is shown that in this case
M is a hyperbolic space form endowed with an exact locally conformal cosymplectic structure. Moreover
T defines an infinitesimal homothety of the connection forms and a relative infinitesimal conformal
transformation of the curvature forms.
The existence of a structure conformal vector field C on M is proved and their properties are
investigated. In the last section, we study the geometry of the tangent bundle of an exact locally conformal
cosymplectic manifold.