论文标题
在切线泊松小组的里曼尼亚几何形状上
On the Riemannian Geometry of tangent Poisson-Lie group
论文作者
论文摘要
令$（g，π_{g}，\ tilde {g}）$为一个配备有左不变的pseudo-riemannian衡量标准$ \ tilde {g} $的泊松组，然后让$（tg，π_{tg} $ g $的组配备了左不变pseudo-riemannian公制$ \ tilde {g}^{c} $，完全提升$ \ tilde {g} $。在本文中，我们分别表达了$（tg，π_{tg}，\ tilde {g}^{c}）$的LEVI-CIVITA连接，曲率和元关节，以Levi-civita的连接，curviTa Connection，curvitator，curvature conterment，curvitator and curvital and curvator and poisson-lie group $ $（g，g，g，g，g，g，g，g，g，g，g，g，g，g，g，g，g，g，g，g，g，g，g，g，我们证明，$ g $上的差分形式的空间$ω^{*}（g）$是一个差分的泊松代数，并且只有$ω^{*}（tg）$是差异分级的poisson代数。此外，我们证明了三胞胎$（g，π_{g}，\ tilde {g}）$是一个伪里人的poisson-lie group，并且只有$（tg，π_{tg} {tg}，\ tilde {g}^{c}^{c}）$也是pseiS-lie，我们也是psse and p。 6维伪里曼尼亚人sanchez de avarez切线泊松小组。
Let $(G,Π_{G},\tilde{g})$ be a Poisson-Lie group equipped with a left invariant pseudo-Riemannian metric $\tilde{g}$ and let $(TG,Π_{TG},\tilde{g}^{c})$ be the Sanchez de Alvarez tangent Poisson-Lie group of $G$ equipped with the left invariant pseudo-Riemannian metric $\tilde{g}^{c}$, complete lift of $\tilde{g}$. In this paper, we express respectively the Levi-Civita connection, curvature and metacurvature of $(TG,Π_{TG},\tilde{g}^{c})$ in terms of the Levi-Civita connection, curvature and metacurvature of the basis Poisson-Lie group $(G,Π_{G},\tilde{g})$ and we prove that the space of differential forms $Ω^{*}(G)$ on $G$ is a differential graded Poisson algebra if, and only if, $Ω^{*}(TG)$ is a differential graded Poisson algebra . Moreover, we prove that the triplet $(G,Π_{G},\tilde{g})$ is a pseudo-Riemannian Poisson-Lie group if, and only if, $(TG,Π_{TG},\tilde{g}^{c})$ is also a pseudo-Riemannian Poisson-Lie group and we give an example of 6-dimensional pseudo-Riemannian Sanchez de Avarez tangent Poisson-Lie group.
