on a finsler manifold, we define conformal vector fields and their complete lifts and prove that incertain conditions they are homothetic.

‎the object of the present paper is to study spacetimes admitting‎ ‎quasi-conformal curvature tensor‎. ‎at first we prove that a quasi-conformally flat spacetime is einstein‎ ‎and hence it is of constant curvature and the energy momentum tensor of such a spacetime satisfying‎ ‎einstein's field equation with cosmological constant is covariant constant‎. ‎next‎, ‎we prove that if the perfect...

‎The object of the present paper is to study spacetimes admitting‎ ‎quasi-conformal curvature tensor‎. ‎At first we prove that a quasi-conformally flat spacetime is Einstein‎ ‎and hence it is of constant curvature and the energy momentum tensor of such a spacetime satisfying‎ ‎Einstein's field equation with cosmological constant is covariant constant‎. ‎Next‎, ‎we prove that if the perfect flui...

Vector fields whose flow preserves a symplectic form up to a constant, such as simple mechanical systems with friction, are called “conformal”. We develop a reduction theory for symmetric conformal Hamiltonian systems, analogous to symplectic reduction theory. This entire theory extends naturally to Poisson systems: given a symmetric conformal Poisson vector field, we show that it induces two r...

We deal with a locally conformal cosymplectic manifoldM(φ,Ω,ξ,η,g) admitting a conformal contact quasi-torse-forming vector field T . The presymplectic 2-form Ω is a locally conformal cosymplectic 2-form. It is shown that T is a 3-exterior concurrent vector field. Infinitesimal transformations of the Lie algebra of ∧M are investigated. The Gauss map of the hypersurfaceMξ normal to ξ is conforma...

Amputation of external legs is carried out explicitly for the conformal invariant three-point function involving two spinors and one vector field. Our results are consistent with the general result that amputing an external leg in a conformal invariant Green function replaces a field by its conformal partner in the Green function. A star-triangle relation involving two spinors and one vector fi...

We deal with a 2m-dimensional Riemannian manifold (M,g) structured by an affine connection and a vector field , defining a -parallel connection. It is proved that is both a torse forming vector field and an exterior concurrent vector field. Properties of the curvature 2-forms are established. It is shown that M is endowed with a conformal symplectic structure Ω and defines a relative conformal ...