Parabolic Geometries I

  title={Parabolic Geometries I},
  author={Jan Slov{\'a}k and Andreas {\vC}ap},
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


(Note: There are no symplectic forms on X unless b and the first Betti number of X have opposite parity.) In a subsequent article with joint authors, a vanishing theorem will be proved for the
The classical concept of affine locally symmetric spaces allows a generalization for various geometric structures on a smooth manifold. We remind the notion of symmetry for parabolic geometries and
On Conformal Geometry.
  • T. Y. Thomas
  • Computer Science
    Proceedings of the National Academy of Sciences of the United States of America
  • 1926
Four functionals on the space of normalized almost Hermitian metrics on almost complex manifolds are discussed and the Euler-Lagrange equations for all these functionals are computed – as a tool for characterizing these metrics.
The Principal Prolongation of First Order G-structures
In this short note we use the concept of the principal prolongation of principal ber bundles to develop an alternative procedure for the construction of prolongations of a class of G-structures of
Octonions, Jordan Algebras and Exceptional Groups
The 1963 Gottingen notes of T. A. Springer are well-known in the field but have been unavailable for some time. This book is a translation of those notes, completely updated and revised. The part of
On non-degenerate real hypersurfaces, graded Lie algebras and Cartan connections
paper we have omitted the proof of Theorem 1 there, because it is essentially achieved by Tanaka [11] and the theorem is now familiar.) Let Mi (i=1, 2) be a real hypersurf ace of a complex manifold
Structure of certain induced representations of complex semisimple Lie algebras
Let £ be a split semisimple Lie algebra over a field <E> of characteristic zero and <£ = 3C+ ]C«eA«£a be the rootspace decomposition of <£ relative to a splitting Cartan subalgebra 5C, where the
Higher order torsions of spaces with Cartan connection
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