伪张量空间中Levi-Civita张量的非协变性和曲率
The Levi-Civita tensor noncovariance and curvature in the pseudotensors space
摘要：
它表明，传统的“协变”的Levi-Civita张量的衍生物是不是真的协变。加上补偿项，就有可能使它协变并等于零。然后，可以在伪张量空间中引入曲率。出现了一个曲率张量，这是不一样的普通的协变项，包括列维-奇维塔密度导数，因此等于零。这一项有点类似于外尔曲率张量中的外尔项。有人试图在组合张量空间（张量加伪张量）中找到一个曲率测度。此外，还利用度规和Levi-Civita密度构造了一些向量，为几何学的发展提供了新的契机。
英文摘要：
It is shown that conventional "covariant" derivative of the Levi-Civita tensor is not really covariant. Adding compensative terms, it is possible to make it covariant and to be equal to zero. Then one can be introduced a curvature in the pseudotensors space. There appears a curvature tensor which is dissimilar to ordinary one by covariant term including the Levi-Civita density derivatives hence to be equal zero. This term is a little bit similar to Weylean one in the Weyl curvature tensor. There has been attempted to find a curvature measure in the combined (tensor plus pseudotensor) tensors space. Besides, there has been constructed some vector from the metric and the Levi-Civita density which gives new opportunities in geometry.
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