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Title
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The bundle of tensor densities and its covariant derivatives
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Author
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Abstract
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| We construct the smooth vector bundle of tensor densities of arbitrary weight in a coordinate-independent way. We prove the general existence of a globally smooth tensor density field, as well as the existence of a globally smooth metric density for a pseudo-Riemannian manifold, specifically. We study the coordinate description of a covariant derivative over densities, and define a natural extension of affine connections to densities. We provide an equivalent characterization, in the case of a pseudo-Riemannian manifold. |
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Language
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English
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Source (journal)
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Axioms
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Publication
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2024
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ISSN
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2075-1680
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DOI
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10.3390/AXIOMS13100667
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Volume/pages
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13
:10
(2024)
, p. 1-17
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Article Reference
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667
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ISI
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001342002000001
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Medium
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E-only publicatie
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Full text (Publisher's DOI)
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Full text (open access)
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