Nonlinear generalized sections of vector bundles

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:440

Article

Nigsch, E. A.¹ 

[1] Univ Vienna, Fac Math, Oskar Morgenstern Pl 1, A-1090 Vienna, Austria

关键词: Nonlinear generalized functions;    Diffeomorphism invariance;    Colombeau algebra;    Singular pseudo-Riemannian geometry;    Covariant derivative;   

DOI  :  10.1016/j.jmaa.2016.03.022

来源: Elsevier

【 摘 要 】

We present an extension of J.F. Colombeau's theory of nonlinear generalized functions to spaces of generalized sections of vector bundles. Our construction builds on classical functional analytic notions, which is the key to having a canonical geometric embedding of vector bundle valued distributions into spaces of generalized sections. This permits to have tensor products, invariance under diffeomorphisms, covariant derivatives and the sheaf property. While retaining as much compatibility to L. Schwartz' theory of distributions as. possible, our theory provides the basis for a rigorous and general treatment of singular pseudo-Riemannian geometry in the setting of Colombeau nonlinear generalized functions. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free