Applications of curved Bernstein-Gelfand-Gelfand sequences (Q2765845)

The author discusses Bernstein-Gelfand-Gelfand sequences and their applications in the conformal geometry. He discusses relations and applications of them in parabolic geometries. He presents examples of BGG sequences for the adjoint representation and SO\((n+1,1)\)-representations. The main result is given by the applications of BGG sequences in Einstein Weyl geometry giving the generalization of Eastwood-Tod Theorem to conformally self-dual Einstein-Weyl manifolds \(M,D\). Then the Faraday curvature \(F^D\) is self-dual, so \(D\) is locally the Levi-Civita connection of an Einstein metric or the Obata connection of a hypercomplex structure.NEWLINENEWLINEFor the entire collection see [Zbl 0973.00041].