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Natural operations in differential geometry
I. Manifolds and Lie Groups.- II. Differential Forms.- III. Bundles and Connections.- IV. Jets and Natural Bundles.- V. Finite Order Theorems.- VI. Methods for Finding Natural Operators.- VII.
Parabolic Geometries I
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
Bernstein-Gelfand-Gelfand sequences
The Bernstein-Gelfand-Gelfand sequences extend the complexes of homogeneous vector bundles to curved Cartan geometries.
Weyl structures for parabolic geometries
Motivated by the rich geometry of conformal Riemannian manifolds and by the recent development of geometries modeled on homogeneous spaces $G/P$ with $G$ semisimple and $P$ parabolic, Weyl structures
Invariant operators on manifolds with almost Hermitian symmetric structures, III. Standard operators
This paper demonstrates the power of the calculus developed in the two previous parts of the series for all real forms of the almost Hermitian symmetric structures on smooth manifolds, including e.g.
INVARIANT OPERATORS OF THE FIRST ORDER ON MANIFOLDS WITH A GIVEN PARABOLIC STRUCTURE
The goal of this paper is to describe explicitly all invariant first order operators on manifolds equipped with parabolic geometries. Both the results and the methods present an essential
Peetre Theorem for Nonlinear Operators
Some generalizations of the well-known Peetre theorem on the locally finite order of support non-increasing R-linear operators, [9, 11], has become a useful tool for various geometrical
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