Connexions conformes sur un fibré vectoriel |
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Authors: | Jean-Louis Milhorat |
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Institution: | Département de Mathématiques et d'Informatique Université des Sciences et Techniques de Nantes 2, rue de la Houssinière 44072, Nantes Cedex 03, France |
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Abstract: | We introduce a new formalism to define conformal connections on a vector bundle, endowed with a conformal class of pseudo-riemannian metrics of signature (p, q). Using a bundle map, called isotropic transformation, we show that these non-linear connections are in one-to-one correspondence with metric connections on an enlarged pseudo-riemannian vector bundle, endowed with a metric of signature (p + 1, q + 1). We then use this formalism to give an intrinsic definition of Cartan's conformal circles. Finally, as an example, we give a geometric interpretation of some results of relativistic electromagnetism, connecting to each electromagnetic field a conformal connection on the tangent bundle of the space-time manifold. |
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