In this paper, we consider generic corank 2 sub-Riemannian structures, and we show that the Spherical Hausdorf measure is always a C^1-smooth volume, which is in fact generically C^2- smooth out of a stratified subset of codimension 7. In particular, for rank 4, it is generically C^2 . This is the continuation of a pre…
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8 results for “corank-2”
The paper finds a geometric explanation for coinciding Thom polynomials of cusp and corank-2 singularities.
problem Explaining the coincidence of Thom polynomials for cusp and corank-2 singularities.
method Analyzing geometrically the coincidence of Thom polynomials for Morin and corank-2 singularities.
result Found a geometric explanation for the coincidence of Thom polynomials for Morin and corank-2 singularities.
The h-principle fails for prelegendrians in fat distributions of corank 2.
problem Investigating the h-principle for fat distributions of corank 2.
method Developed the theory of prelegendrians, including front projection and pseudoholomorphic curve invariants.
result Found an infinite family of non-prelegendrian isotopic tori in the standard fat distribution.
Canonical frames for distributions of odd rank and corank 2 with maximal first Kronecker indexmath.DG
We construct canonical frames and find all maximally symmetric models for a natural generic class of corank 2 distributions on manifolds of odd dimension greater or equal to 7. This class of distributions is characterized by the following two conditions: the pencil of 2-forms associated with the corresponding Pfaffian …
We study a moduli stratum of A-orbits of plane-to-plane germs of corank 2 with codimension 3. We describe explicitly the bifurcation diagram of its topologically A-versal unfolding. Two geometric applications to parabolic objects are presented.
Study horizontal discs in fat distributions, proving their existence.
problem Existence of embedded horizontal discs in fat distributions.
method Analyzing nonlinear PDEs and proving local invertibility.
result Existence of germs of embedded horizontal discs.
Characterizes GM-groups via sub-Riemannian geometry properties.
problem Characterizing step-two Carnot groups via sub-Riemannian geometry.
method Sub-Riemannian geometric properties, including squared distance, cut locus, optimal synthesis.
result Characterization of GM-groups and exact expression of for classical cut locus.
The article proves the existence of horizontal immersions into fat distributions and contact structures.
problem Proving the existence of horizontal immersions in fat distributions and contact structures.
method Gromov's sheaf theoretic and analytic techniques of -principle.
result Existence of horizontal immersions of an arbitrary manifold into degree 2 fat distributions and quaternionic contact structures.