A classification of Monge-Ampère equations
A construction of non-flat non-homogeneous symmetric parabolic geometries
We construct series of examples of non-flat non-homogeneous parabolic geometries that carry a symmetry of the parabolic geometry at each point.
A recursion operator for the universal hierarchy equation via Cartan’s method of equivalence
We apply Cartan’s method of equivalence to find a Bäcklund autotransformation for the tangent covering of the universal hierarchy equation. The transformation provides a recursion operator for symmetries of this equation.
Almost product structures and Monge-Ampère equations.
-symmetries and reduction of equations without Lie point symmetries.
Circular symmetry and the trace formula.
Classification of differential invariant submodels.
Classification of Monge-Ampère equations with two variables
This paper deals with the classification of hyperbolic Monge-Ampère equations on a two-dimensional manifold. We solve the local equivalence problem with respect to the contact transformation group assuming that the equation is of general position nondegenerate type. As an application we formulate a new method of finding symmetries. This together with previous author's results allows to state the solution of the classical S. Lie equivalence problem for the Monge-Ampère equations.
Comportement asymptotique des valeurs propres du laplacien sur un ouvert à bord fractal
Conservation laws for equations related to soil water equations.
Contact geometry of hyperbolic equations of generic type.
Contact geometry of hyperbolic Monge-Ampére equations.
Convexity for invariant differential operators on semisimple symmetric spaces
Crochet de Jacobi non local sur un revêtement et ses applications à l’étude de l’équation de Burgers
Curved Casimir operators and the BGG machinery.
Differential invariants of generic hyperbolic Monge-Ampère equations
In this paper basic differential invariants of generic hyperbolic Monge-Ampère equations with respect to contact transformations are constructed and the equivalence problem for these equations is solved.
Eigenspaces of Invariant Differential Operators on an Affine Symmetric Space.
Ellipticity of the symplectic twistor complex
For a Fedosov manifold (symplectic manifold equipped with a symplectic torsion-free affine connection) admitting a metaplectic structure, we shall investigate two sequences of first order differential operators acting on sections of certain infinite rank vector bundles defined over this manifold. The differential operators are symplectic analogues of the twistor operators known from Riemannian or Lorentzian spin geometry. It is known that the mentioned sequences form complexes if the symplectic...
Équations de Monge-Ampère invariantes sur les variétés Riemanniennes compactes
Espaces symétriques et méthode de Kashiwara-Vergne