Abstract
We construct an algebra of nonlinear generalized tensor fields on manifolds in the sense of Colom\-beau, i.e., containing distributional tensor fields as a linear subspace and smooth tensor fields as a faithful subalgebra. The use of a background connection on the manifold allows for a simplified construction based on the existing scalar theory of full diffeomorphism invariant Colombeau algebras on manifolds, still having a canonical embedding of tensor distributions. In the particular case of the Levi-Civita connection on Riemannian manifolds, one obtains that this embedding commutes with pullback along homotheties and Lie derivatives along Killing vector fields only.
Citation
Eduard Nigsch. "Nonlinear tensor distributions on Riemannian manifolds." Rocky Mountain J. Math. 44 (2) 649 - 683, 2014. https://doi.org/10.1216/RMJ-2014-44-2-649
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