Essential Killing fields of parabolic geometries: projective and conformal structures

Andreas Čap; Karin Melnick

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Editors’ preface for the topical issue “Finite dimensional integrable systems, dynamics, and Lie theoretic methods in Geometry and Mathematical Physics”

Andreas Čap, Vladimir Matveev, Karin Melnick, Galliano Valent (2012)

Open Mathematics

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Submanifold geometry in generalized flag manifolds

Burstall, Francis E., Calderbank, David M. J.

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Two constructions with parabolic geometries

Čap, Andreas

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Homogeneous Cartan geometries

Matthias Hammerl (2007)

Archivum Mathematicum

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We describe invariant principal and Cartan connections on homogeneous principal bundles and show how to calculate the curvature and the holonomy; in the case of an invariant Cartan connection we give a formula for the infinitesimal automorphisms. The main result of this paper is that the above calculations are purely algorithmic. As an example of an homogeneous parabolic geometry we treat a conformal structure on the product of two spheres.