Rocky Mountain Journal of Mathematics

Nonlinear tensor distributions on Riemannian manifolds

Eduard Nigsch

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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.

Article information

Source
Rocky Mountain J. Math., Volume 44, Number 2 (2014), 649-683.

Dates
First available in Project Euclid: 4 August 2014

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1407154918

Digital Object Identifier
doi:10.1216/RMJ-2014-44-2-649

Mathematical Reviews number (MathSciNet)
MR3240518

Zentralblatt MATH identifier
1311.46042

Subjects
Primary: 46F30: Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.)
Secondary: 46T30: Distributions and generalized functions on nonlinear spaces [See also 46Fxx]

Keywords
Tensor distribution nonlinear generalized function Colombeau algebra connection

Citation

Nigsch, Eduard. Nonlinear tensor distributions on Riemannian manifolds. Rocky Mountain J. Math. 44 (2014), no. 2, 649--683. doi:10.1216/RMJ-2014-44-2-649. https://projecteuclid.org/euclid.rmjm/1407154918


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