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Exterior Differential Systems
Basic theorems Cartan-Khler theory linear differential systems the characteristic variety prolongation theory applications of commutative algebra and algebraic geometry to the study of exteriorExpand
Existence theorems for analytic linear partial differential equations
The theory of analytic systems of partial differential equations was first systematically investigated by Riquier and Elie Cartan around 1900. The existence of local solutions involves an algebraicExpand
The Hamilton-Cartan formalism in the calculus of variations
In this paper, we give an exposition of the geometry of the calculus of variations in several variables. The main emphasis is on the Hamiltonian formalism via the use of a linear differential formExpand
ZERO-ENERGY FIELDS ON COMPLEX PROJECTIVE SPACE
We consider complex projective space with its Fubini–Study metric and the X-ray transform defined by integration over its geodesics. We identify the kernel of this transform acting on symmetricExpand
Regularity Theorems in Riemannian Geometry. II. Harmonic Curvature and the Weyl Tensor
We study the regularity of metrics satisfying geometric conditions imposed on the Ricci or Weyl curvatures. In particular, we show that a metric with harmonic curvature is realanalytic in harmonicExpand
Linear Differential Systems
TLDR
The goal of this chapter is to develop the formalism of linear Pfaffian differential systems in a form that will facilitate the computation of examples. Expand
Prolongations of linear partial differential equations. II. Inhomogeneous equations
© Gauthier-Villars (Éditions scientifiques et médicales Elsevier), 1968, tous droits réservés. L’accès aux archives de la revue « Annales scientifiques de l’É.N.S. » (http://www.Expand
Prolongations of linear partial differential equations. I. A conjecture of Élie Cartan
© Gauthier-Villars (Éditions scientifiques et médicales Elsevier), 1968, tous droits réservés. L’accès aux archives de la revue « Annales scientifiques de l’É.N.S. » (http://www.Expand
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