On Some Properties Of The Reeb Vector Field Of A Finsler Manifold

Riemann-Finsler geometry is an important branch of differential geometry and has along history. In this paper, we firstly recall some basic properties about Killing vectorfields and conformal vector fields on a Riemannian manifold M; then for any smoothvector fields X, Y on M, we compute the negative gradient vector field fand theLaplacian fof f=<X,Y>, and by using these results, we discuss the Reeb vectorfields on a Finsler manifold; finally we give some characterizations of a Finsler manifoldof constant flag curvature1.