The object of study are almost paracomplex pseudo-Riemannian manifolds with a pair of metrics associated each other by the almost paracomplex structure. A torsion-free connection and tensors with geometric interpretation are found which are invariant under the twin interchange, i.e. the swap of the counterparts of the pair of associated metrics and the corresponding Levi-Civita connections. A Lie group depending on two real parameters is constructed as an example of a four-dimensional manifold of the studied type and the mentioned invariant objects are found in an explicit form.

中文翻译：

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几乎超复杂的伪-黎曼流形上相关度量对的孪生交换下的不变张量

研究的对象是几乎超复杂的伪黎曼流形，它们具有通过几乎超复杂结构相互关联的一对度量。发现在双互换下不变的无扭转连接和张量具有几何解释，即在一对关联度量对的对应物和相应的Levi-Civita连接之间的互换。构造了一个依赖于两个实际参数的李群作为研究类型的多维流形的一个例子，并以显式形式找到了所述不变对象。