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International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 2, Pages 267-278
http://dx.doi.org/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 Hindawi Publishing Corporation. 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 η0 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.