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Nonlinear generalised functions on manifolds

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)

Record type: Article

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
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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
ORCID for James A. Vickers: ORCID iD orcid.org/0000-0002-1531-6273

Catalogue record

Date deposited: 25 Oct 2019 16:30
Last modified: 15 May 2020 00:26

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