论文标题
$α$ - 一般几何连接
$α$-connections in generalized geometry
论文作者
论文摘要
我们考虑一个由$α$ - 连接的家族，由一对通用的双准准统计连接$（\ hat {\ nabla}，\ hat {\ nabla}^*）$上的一般切线bundle $（tm \ oplus t^*m t^*m，\ cechblus t^*m，\ he {此外，我们为$ \ hat \ nabla^*$提供了必要的条件，使其成为Equiaffine连接，我们证明，如果$ h $是对称的，并且$ \ nabla h = 0 $，则$（tm \ oplus t^*m，\ oplus t^*m，\ check {h} \ hat {\ nabla}^{（ - α）}）$是一种共轭ricci-对称歧管。同样，我们表征了广义几乎几乎复合物和通用金属结构W.R.T.由$α$ - 连接定义的支架。最后，我们研究了$α$ - 连接由伪 - riemannian歧管的双重公制定义的，$（m，g）$，具有非脱位$ g $ g $ -smmetric $（1,1）$ - 张量 - 张量 - 张量$ j $，因此$ d^\ nabla j = 0 $ \ nabla $ \ nabla $ g $ g $ g $ g。
We consider a family of $α$-connections defined by a pair of generalized dual quasi-statistical connections $(\hat{\nabla},\hat{\nabla}^*)$ on the generalized tangent bundle $(TM\oplus T^*M, \check{h})$ and determine their curvature, Ricci curvature and scalar curvature. Moreover, we provide the necessary and sufficient condition for $\hat \nabla^*$ to be an equiaffine connection and we prove that if $h$ is symmetric and $\nabla h=0$, then $(TM\oplus T^*M, \check{h}, \hat{\nabla}^{(α)}, \hat{\nabla}^{(-α)})$ is a conjugate Ricci-symmetric manifold. Also, we characterize the integrability of a generalized almost product, of a generalized almost complex and of a generalized metallic structure w.r.t. the bracket defined by the $α$-connection. Finally we study $α$-connections defined by the twin metric of a pseudo-Riemannian manifold, $(M,g)$, with a non-degenerate $g$-symmetric $(1,1)$-tensor field $J$ such that $d^\nabla J=0$, where $\nabla$ is the Levi-Civita connection of $g$.
