Nonlinear generalised functions on manifolds
Nonlinear generalised functions on manifolds
This paper lays the foundations for a nonlinear theory of differential geometry that is developed in a subsequent paper which is based on Colombeau algebras of tensor distributions on manifolds. We adopt a new approach and construct a global theory of algebras of generalised functions on manifolds based on the concept of smoothing operators. This produces a generalisation of previous theories in a form which is suitable for applications to differential geometry. The generalised Lie derivative is introduced and shown to commute with the embedding of distributions. It is also shown that the covariant derivative of a generalised scalar field commutes with this embedding at the level of association.
math.FA, gr-qc, math.DG, 46F30, 46T30
Nigsch, Eduard A.
ea9b17e3-8ab7-4222-b1b3-a9e0e428634e
Vickers, James A.
719cd73f-c462-417d-a341-0b042db88634
Nigsch, Eduard A.
ea9b17e3-8ab7-4222-b1b3-a9e0e428634e
Vickers, James A.
719cd73f-c462-417d-a341-0b042db88634
Nigsch, Eduard A. and Vickers, James A.
(2019)
Nonlinear generalised functions on manifolds.
arXiv.
(In Press)
Abstract
This paper lays the foundations for a nonlinear theory of differential geometry that is developed in a subsequent paper which is based on Colombeau algebras of tensor distributions on manifolds. We adopt a new approach and construct a global theory of algebras of generalised functions on manifolds based on the concept of smoothing operators. This produces a generalisation of previous theories in a form which is suitable for applications to differential geometry. The generalised Lie derivative is introduced and shown to commute with the embedding of distributions. It is also shown that the covariant derivative of a generalised scalar field commutes with this embedding at the level of association.
Text
1910.03411
- Accepted Manuscript
More information
Accepted/In Press date: 8 October 2019
Keywords:
math.FA, gr-qc, math.DG, 46F30, 46T30
Identifiers
Local EPrints ID: 435184
URI: http://eprints.soton.ac.uk/id/eprint/435184
PURE UUID: 6fe8a80e-ef99-4425-8f3c-5b551a62612d
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Date deposited: 25 Oct 2019 16:30
Last modified: 17 Mar 2024 02:32
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Contributors
Author:
Eduard A. Nigsch
Author:
James A. Vickers
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