近Leibniz流形的判定及应用

Judgement and Application of Almost Leibniz Manifolds

为进一步完善近Leibniz流形的理论,从张量的角度研究了Leibniz流形及近Leibniz流形,给出了Leibniz流形的张量表示形式,并用该张量形式表示了Leibniz流形和近Leibniz流形上的动力系统,然后给出一个近Leibniz流形是Leibniz流形的判定条件,且把它应用在近Leibniz动力系统上。

To perfect the theories of almost Leibniz manifold profoundly,Leibniz manifold and almost Leibniz manifold are studied from point of tensor,and the forms of tensor of Leihniz manifold are given,so dynamical systems on Leibniz manifold and almost Leibniz manifold can be given according to tensors. Then a qualification that ahnost Leibniz manifold is a Leibniz manifold is given, finally apply it to almost Leibniz dynamical systems.