Title : The bundle of Weyl structures associated to an AHS structure.
Speaker: Andreas Cap
Affiliation: University of Vienna
Time: 10am Friday, 1 March, 2019
Location: 303e.257
Abstract
This talk reports on joint work in progress with Thomas Mettler (Frankfurt), which generalizes a construction of Dunajski and Mettler for projective structures. We work in the setting of AHS structures (parabolic geometries associated to |1|-gradings). Given such a structure on a manifold $M$, we construct and affine bundle $A\to M$, whose smooth sections are in bijective correspondence with Weyl structures for the initial AHS structure. On the manifold $A$, one obtains a natural almost bi-Lagrangean structure, which combines an almost symplectic structures and a pseudo-Riemannian metric of split signature and carries a natural connection. There is an efficient calculus relating this geometry to the AHS structure. Using this we show that the is symplectic iff the initial AHS structure is torsion-free and that in this case one obtains an Einstein metric. In the end of the talk, I'll indicate a relation to fully non-linear invariant PDE.

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