Casimir Function on Leibniz Manifolds

The effects of diffeomorphism and Leibniz mapping on Casimir function of Leibniz manifolds are investigated, which finds the following conclusions： (1) Casimir function C（x） on Leibniz manifolds (M,·，·M)，can be induced by diffeomorphism φ∶M→N to a Casimir function (φ-１)*C on N; (2) with invertible Leibniz mapping Ψ∶M→N, the linear combination of No’s Casimir functions ∑si=1λiCion N, can be pulled back into a Casimir function on M. Finally, several formulas concerning Leibniz vector field and Casimir function are presented.