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Summary: Let ${\germ g}$ be a real semisimple $|k|$-graded Lie algebra such that the Lie algebra cohomology group $H^1({\germ g}_-,{\germ g})$ is contained in negative homogeneous degrees. We show that if we choose $G= \operatorname{Aut}({\germ g})$ and denote by $P$ the parabolic subgroup determined by the grading, there is an equivalence between regular, normal parabolic geometries of type $(G,P)$ and filtrations of the tangent bundle, such that each symbol algebra $\text{gr}(T_xM)$ is isomorphic to the graded Lie algebra ${\germ g}_-$. Examples of parabolic geometries determined by filtrations of the tangent bundle are discussed. (English) |
