Two constructions with parabolic geometries
By Andreas Čap. 2005
52 citations recorded by the source corpus.
This is an expanded version of a series of lectures delivered at the 25th Winter School ``Geometry and Physics'' in Srni. After a short introduction to Cartan geometries and parabolic geometries, we give a detailed description of the equivalence between parabolic geometries and underlying geometric structures. The second part of the paper is devoted to constructions which relate parabolic geometries of different type. First we discuss the construction of correspondence spaces and twistor spaces, which is related to nested parabolic subgroups in the same semisimple Lie group. An example related to twistor theory for Grassmannian structures and the geometry of second order ODE's is discussed in detail. In the last part, we discuss analogs of the Fefferman construction, which relate geometries corresponding different semisimple Lie groups.
Subfields: Algebra and Number Theory, Astronomy and Astrophysics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/db1de4cd83b5fc1f682ba1785b8e9cf10e7405d0
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Citations in the corpus
- Maximally homogeneous para-CR manifolds of semisimple type (2006, unknown): “33 (see [BDS77], [Ku97], [C02] and [ C05 ]). Inspired by the close link and the analogies the Feerman construction provides between CR geometry and conformal Lorentzian geometry there is now a growing number of geometric and analytic investigations of Feerman spaces.”
- Infinitesimal automorphisms and deformations of parabolic geometries (2005, background): “A description of this equivalence can be found in [7].”