Leibniz流形上的几种运算

Discussion over Some Operations on Leibniz Manifolds

通过Leibniz代数的理论来研究Leibniz流形上的运算.首先验证了Leibniz流形上分级张量代数是Leibniz代数,然后由Leibniz代数理论给出Leibniz流形上的三种运算及其性质,为深入研究Leibniz流形理论提供了运算工具,从而进一步完善了Leibniz流形的理论。

Some operations of Leibniz manifold are studied by using theories of Leibniz algebra.First,it is verified that graded tensor algebra on Leibniz manifold is Leibniz algebra,then three operantions of Leibniz manifold and some properties of them are given,which serve as the computing tools for in-depth Leibniz manifold theories study.Thus the theories of Leibniz manifold are further perfected.