In this paper, we provide some results on Poisson manifold (M, Π) with contravariant Levi–Civita connection associated to pair (Π, g). We introduce the notion of Einstein Poisson warped product space (M = B _f F, Π, g ^f ) (where Π = Π₁ + Π₂). Moreover, we show that if M is an Einstein Poisson warped product space with nonpositive scalar curvature and compact base B, J ₁ is a field endomorphism on T*B satisfies , then M is simply a Riemannian Poisson product. For a contravariant Lorentzian Poisson warped space (M = B _f F, g, Π) (where ) one can determine contravariant Einstein equations and the cosmological constant Λ corresponding to the contravariant Einstein equation G = −Λg. Moreover, it is shown that Einstein equation G = −Λg, induces the contravariant Einstein equation with cosmological constant Λ _F on fiber space (F, g _F , Π _F ).

在本文中，我们提供了一些关于泊松流形 ( M , Π ) 的结果，其中逆变 Levi-Civita 连接与对 (Π, g ) 相关联。我们引入了爱因斯坦泊松扭曲积空间的概念（M = B _f F , Π, g ^f）（其中 Π = Π ₁ + Π ₂）。此外，我们证明如果M是具有非正标量曲率和紧基B的爱因斯坦泊松翘积空间，则J _1是T * B上的场自同态，则M 只是黎曼泊松积。对于逆变洛伦兹泊松扭曲空间 ( M = B _f F , g , Π)（其中），可以确定逆变爱因斯坦方程和对应于逆变爱因斯坦方程G = -Λ g的宇宙学常数 Λ 。此外，还表明爱因斯坦方程G = -Λ g在纤维空间 ( F , g _F , Π _F )上导出了具有宇宙学常数 Λ _F的逆变爱因斯坦方程。