Parabolic Geometries I

@inproceedings{Slovk2009ParabolicGI,
  title={Parabolic Geometries I},
  author={Jan Slov{\'a}k and Andreas {\vC}ap},
  year={2009}
}
The first monograph on parabolic geometry in the literature following several ground-braking results achieved by the authors and their collaborators in the last two decades. The volume will be followed by the second one focused on mathematical applications 
Essential Killing fields of parabolic geometries: projective and conformal structures
We use the general theory developed in our article [Čap A., Melnick K., Essential Killing fields of parabolic geometries, Indiana Univ. Math. J. (in press)], in the setting of parabolic geometries to
Curvature without connection
We show that the theory of geometric structures proposed in the recent book "An Alternative Approach to Lie Groups and Geometric Structures" can be developed independently of connections.
Ricci Curvature and the Mechanics of Solids
We discuss some differential geometry pertaining to continuum mechanics and the route recently taken by D.N. Arnold, R.S. Falk, and R. Winther in deriving new improved finite element schemes in
Parabolic symmetric spaces
We study here systems of symmetries on |1|-graded parabolic geometries. We are interested in smooth systems of symmetries, and we discuss non-flat homogeneous |1|-graded geometries. We show the
The canonical Cartan bundle and connection in CR geometry
  • M. Herzlich
  • Mathematics
    Mathematical Proceedings of the Cambridge Philosophical Society
  • 2009
Abstract We give a simple differential geometric description of the canonical Cartan (or tractor) bundle and connection in CR geometry, thus offering an alternative definition to the usual abstract
Notes on connections attached to A-structures
Geometry of curves in generalized flag varieties
The current paper is devoted to the study of integral curves of constant type in generalized flag varieties. We construct a canonical moving frame bundle for such curves and give a criterion when it
Holomorphic Parabolic Geometries and Calabi{Yau Manifolds
We prove that the only complex parabolic geometries on Calabi{Yau manifolds are the homogeneous geometries on complex tori. We also classify the complex parabolic geometries on homogeneous compact
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