We extend the construction of the authors' paper of 2002 by introducing spaces ofgeneralized tensor fields on smooth manifolds that possess optimalembedding and consistency properties with spaces of tensordistributions in the sense of L. Schwartz. We thereby obtain auniversal algebra of generalized tensor fields canonically containingthe space of distributional tensor fields. The canonicalembedding of distributional tensor fields also commutes with the Liederivative. This constructionprovides the basis for applications of algebras of generalizedfunctions in nonlinear distributional geometry and, in particular,to the study of spacetimes of low differentiability in generalrelativity.
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