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Abstract: It is shown that conventional -covariant- derivative of the Levi-Civitatensor is not really covariant. Adding compensative terms, it is possible tomake it covariant and to be equal to zero. Then one can be introduced acurvature in the pseudotensors space. There appears a curvature tensor which isdissimilar to ordinary one by covariant term including the Levi-Civita densityderivatives hence to be equal zero. This term is a little bit similar toWeylean one in the Weyl curvature tensor. There has been attempted to find acurvature measure in the combined tensor plus pseudotensor tensors space.Besides, there has been constructed some vector from the metric and theLevi-Civita density which gives new opportunities in geometry.



Author: A. L. Koshkarov University of Petrozavodsk, Physics department, Russia

Source: https://arxiv.org/







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