Weyl structures for parabolic geometries

Details Weyl structures for parabolic geometries Weyl structures for parabolic geometries

2000-01-28

arxiv.org/abs/math/0001166v1

Mathematics

Differential Geometry

26 pages

Scientific paper

Motivated by the rich geometry of conformal Riemannian manifolds and by the recent development of geometries modeled on homogeneous spaces $G/P$ with $G$ semisimple and $P$ parabolic, Weyl structures and preferred connections are introduced in this general framework. In particular, we extend the notions of scales, closed and exact Weyl connections, and Rho--tensors, we characterize the classes of such objects, and we use the results to give a new description of the Cartan bundles and connections for all parabolic geometries.

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