A constructive approach to bundles of geometric objects of finite rank on a differentiable manifold is proposed, whereby the standard techniques of fiber bundle theory are extensively used. Both the point of view of transition functions (here directly constructed from the jets of local diffeomorphisms of the basis manifold) and that of principal fiber bundles are developed in detail. These, together with the absence of any reference to the current functorial approach, provide a natural clue from the point of view of physical applications. Several examples are discussed. In the last section the functorial approach is also presented in a constructive way, and the Lie derivative of a field of geometric objects is defined. © 1983 American Institute of Physics.

A constructive approach to bundles of geometric objects on a differentiable manifold / Ferraris, M.; Francaviglia, M.; Reina, Cesare. - In: JOURNAL OF MATHEMATICAL PHYSICS. - ISSN 0022-2488. - 24:1(1983), pp. 120-124. [10.1063/1.525580]

A constructive approach to bundles of geometric objects on a differentiable manifold

Reina, Cesare
1983

Abstract

A constructive approach to bundles of geometric objects of finite rank on a differentiable manifold is proposed, whereby the standard techniques of fiber bundle theory are extensively used. Both the point of view of transition functions (here directly constructed from the jets of local diffeomorphisms of the basis manifold) and that of principal fiber bundles are developed in detail. These, together with the absence of any reference to the current functorial approach, provide a natural clue from the point of view of physical applications. Several examples are discussed. In the last section the functorial approach is also presented in a constructive way, and the Lie derivative of a field of geometric objects is defined. © 1983 American Institute of Physics.
24
1
120
124
Ferraris, M.; Francaviglia, M.; Reina, Cesare
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/61054
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