Rocky Mountain Journal of Mathematics
- Rocky Mountain J. Math.
- Volume 44, Number 2 (2014), 649-683.
Nonlinear tensor distributions on Riemannian manifolds
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.
Rocky Mountain J. Math., Volume 44, Number 2 (2014), 649-683.
First available in Project Euclid: 4 August 2014
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 46F30: Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.)
Secondary: 46T30: Distributions and generalized functions on nonlinear spaces [See also 46Fxx]
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