Connexions conformes sur un fibré vectoriel
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.
- Publication:
-
Journal of Geometry and Physics
- Pub Date:
- 1989
- DOI:
- 10.1016/0393-0440(89)90026-0
- Bibcode:
- 1989JGP.....6..559M
- Keywords:
-
- Groupe conforme;
- Groupe et espace de Möbius;
- Transformation isotropique;
- Connexion généralisée conforme