On the Prolongations of Differentiable Distributions
On the transversal distribution and the complete figure in the second order multiple integral problem in the calculus of variations.
On the transversal distribution and the complete figure in the second order multiple integral problem in the calculus of variations.
Parametric homotopy principle of some partial differential relations
Pierrot's theorem for singular Riemannian foliations.
Let F be a singular Riemannian foliation on a compact connected Riemannian manifold M. We demonstrate that global foliated vector fields generate a distribution tangent to the strata defined by the closures of leaves of F and which, in each stratum, is transverse to these closures of leaves.
Reduction in contact geometry.
Regularity conditions for liftings of functions and vector fields to natural bundles
Rigid paths of generic 2-distributions with degenerate points on 3-manifolds
We study rigid paths of generic 2-distributions with degenerate points on 3-manifolds. A complete description of such paths is obtained. For the proof, we construct separating surfaces of paths admissible for distributions.
Semi-rigid CR structures and holomorphic extendability
Simple germs of corank one affine distributions
Singularities and normal forms of generic 2-distributions on 3-manifolds
We give a complete classification of germs of generic 2-distributions on 3-manifolds. By a 2-distribution we mean either a module generated by two vector fields (at singular points its dimension decreases) or a Pfaff equation, i.e. a module generated by a differential 1-form (at singular points the dimension of its kernel increases).
Singularities and normal forms of smooth distributions
In this expository paper we present main results (from classical to recent) on local classification of smooth distributions.
Singularity classes of special 2-flags.
Some results on the frame bundle of an almost contact metric manifold
Split octonions and generic rank two distributions in dimension five
In his famous five variables paper Elie Cartan showed that one can canonically associate to a generic rank 2 distribution on a 5 dimensional manifold a Cartan geometry modeled on the homogeneous space , where is one of the maximal parabolic subgroups of the exceptional Lie group . In this article, we use the algebra of split octonions to give an explicit global description of the distribution corresponding to the homogeneous model.
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.
Sub-Riemannian Metrics: Minimality of Abnormal Geodesics versus Subanalyticity
We study sub-Riemannian (Carnot-Caratheodory) metrics defined by noninvolutive distributions on real-analytic Riemannian manifolds. We establish a connection between regularity properties of these metrics and the lack of length minimizing abnormal geodesics. Utilizing the results of the previous study of abnormal length minimizers accomplished by the authors in [Annales IHP. Analyse nonlinéaire 13, p. 635-690] we describe in this paper two classes of the germs of distributions (called 2-generating...
Superfixed positions in the geometry of Goursat flags.
Synge-Beil and Riemann-Jacobi jet structures with applications to physics.
The almost Einstein operator for distributions
For the geometry of oriented distributions , which correspond to regular, normal parabolic geometries of type for a particular parabolic subgroup , we develop the corresponding tractor calculus and use it to analyze the first BGG operator associated to the -dimensional irreducible representation of . We give an explicit formula for the normal connection on the corresponding tractor bundle and use it to derive explicit expressions for this operator. We also show that solutions of this operator...