Weyl structures for parabolic geometries

Warning

This publication doesn't include Institute of Computer Science. It includes Faculty of Science. Official publication website can be found on muni.cz.

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