Weyl structures for parabolic geometries

2000/01/28 by Andreas Cap, Cap, Andreas, Jan Slovak +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #math.DG

paper · pdf · doi:10.48550/arxiv.math/0001166

26 pages

arxiv created 2000/01/28 · arxiv updated 2009/11/30

Abstract

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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