Conformal vector fields on almost co-Kähler manifolds

In this paper, we characterize almost co-Kähler manifolds with a conformal vector field. It is proven that if an almost co-Kähler manifold has a conformal vector field that is collinear with the Reeb vector field, then the manifold is a K-almost co-Kähler manifold. It is also shown that if a (κ, μ)-almost co-Kähler manifold admits a Killing vector field V, then either the manifold is K-almost co-Kähler or the vector field V is an infinitesimal strict contact transformation, provided that the (1,1) tensor h remains invariant under the Killing vector field.

Conformal Vector Fields and the De-Rham Laplacian on a Riemannian Manifold

We study the effect of a nontrivial conformal vector field on the geometry of compact Riemannian spaces. We find two new characterizations of the m-dimensional sphere Sm(c) of constant curvature c. The first characterization uses the well known de-Rham Laplace operator, while the second uses a nontrivial solution of the famous Fischer–Marsden differential equation.

Classification of proper teleparallel conformal symmetry of spherically symmetric static spacetimes using diagonal tetrads

We study proper teleparallel conformal vector fields in spherically symmetric static spacetimes. The main objective of this paper is to present the classification for the above-mentioned spacetimes. The problem has been examined by two methods: direct integration technique and diagonal tetrads. We show that the spherically symmetric static spacetimes do not admit proper teleparallel conformal vector field, so are actually the teleparallel killing vector fields.

Closed conformal vector fields on pseudo-Riemannian manifolds

We give here a geometric proof of the existence of certain local coordinates on a pseudo-Riemannian manifold admitting a closed conformal vector field.

On a class of exact locally conformal cosymlectic manifolds

An almost cosymplectic manifoldMis a(2m+1)-dimensional oriented Riemannian manifold endowed with a 2-formΩof rank2m, a 1-formηsuch thatΩm Λ η≠0and a vector fieldξsatisfyingiξΩ=0andη(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 fieldTsuch that the Riemannian connection is parallel with respect toT. It is shown that in this caseMis a hyperbolic space form endowed with an exact locally conformal cosymplectic structure. MoreoverTdefines an infinitesimal homothety of the connection forms and a relative infinitesimal conformal transformation of the curvature forms.The existence of a structure conformal vector fieldConMis 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.