Leibniz流形上Casimir函数

Casimir Function on Leibniz Manifolds

摘要: 通过研究微分同胚及Leibniz映射对Leibniz流形上Casimir函数的作用,得出了:(1) Leibniz流形(M,·,·M)上的Casimir函数C(x),可以由微分同胚φ:M→N诱导为N上的Casimir函数(φ-1)*C;(2)可逆的Leibniz映射ψ:M→N,可以把N上的Casimir函数的线性组合∑si=1λiCi拉回为M上的Casimir函数．最后给出了Leibniz向量场和Casimir函数间的几个公式．

Abstract: 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.