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.
Related projects:	Differential geometry of higher order Mathematical structures of algebra and geometry