Weyl structures for parabolic geometries

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Authors

SLOVÁK Jan CAP Andreas

Year of publication 2003
Type Article in Periodical
Magazine / Source Mathematica Scandinavica
MU Faculty or unit

Faculty of Science

Citation
Field General mathematics
Keywords Cartan Connection; Parabolic Geometry; Weyl Structure; Conformal Geometry
Description 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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