On formal theory of differential equations. II.
On geometry of curves of flags of constant type
We develop an algebraic version of Cartan’s method of equivalence or an analog of Tanaka prolongation for the (extrinsic) geometry of curves of flags of a vector space W with respect to the action of a subgroup G of GL(W). Under some natural assumptions on the subgroup G and on the flags, one can pass from the filtered objects to the corresponding graded objects and describe the construction of canonical bundles of moving frames for these curves in the language of pure linear algebra. The scope...
On super (or pseudo) differential forms as superfunctions
On the higher order Poincaré-Cartan forms
On the projective structure of a real hypersurface in C...
On transitive submanifolds of and
Poincaré-Cartan forms in higher order variational calculus on fibred manifolds.
The aim of the present work is to present a geometric formulation of higher order variational problems on arbitrary fibred manifolds. The problems of Engineering and Mathematical Physics whose natural formulation requires the use of second order differential invariants are classic, but it has been the recent advances in the theory of integrable non-linear partial differential equations and the consideration in Geometry of invariants of increasingly higher orders that has highlighted the interest...
Rank-2 distributions satisfying the Goursat condition : all their local models in dimension 7 and 8
Rank-2 distributions satisfying the Goursat condition: all their local models in dimension 7 and 8
We study the rank–2 distributions satisfying so-called Goursat condition (GC); that is to say, codimension–2 differential systems forming with their derived systems a flag. Firstly, we restate in a clear way the main result of[7] giving preliminary local forms of such systems. Secondly – and this is the main part of the paper – in dimension 7 and 8 we explain which constants in those local forms can be made 0, normalizing the remaining ones to 1. All constructed equivalences are explicit. ...
Recent advances in the theory of holonomy
Régularité et non régularité des solutions non strictement convexes de l'équation de Monge-Ampère
Regularity of differential forms minimizing degenerate elliptic functionals.
Remark on local existence of -structure with prescribed structural functions on a manifold of dimension two
Remarques sur les idéaux de polynômes et de formes différentielles extérieures I
Remarques sur les idéaux de polynômes et de formes différentielles extérieures II
Singularités d'ordre supérieur de 1-formes, 2-formes et équations de Pfaff
Smooth singular solutions of hyperplane fields. I
Smooth singular solutions of hyperplane fields. II
Some results on the calculus of variations on jet spaces
Stability of certain Engel-like distributions
We introduce a higher dimensional analogue of the Engel structure, motivated by the Cartan prolongation of contact manifolds. We study the stability of such structure, generalizing the Gray-type stability results for Engel manifolds. We also derive local normal forms defining such a distribution.