Related papers: Contact Geometry of Hyperbolic Equations of Generi…
In this poster, we present a model of large extra dimensions where the internal space has the geometry of a hyperbolic disc. Compared with the ADD model, this model provides a more satisfactory solution to the hierarchy problem between the…
We define an almost--cosymplectic--contact structure which generalizes cosymplectic and contact structures of an odd dimensional manifold. Analogously, we define an almost--coPoisson--Jacobi structure which generalizes a Jacobi structure.…
A numerical scheme is developed for solution of the Goursat problem for a class of nonlinear hyperbolic systems with an arbitrary number of independent variables. Convergence results are proved for this difference scheme. These results are…
In the article differential-difference (semi-discrete) lattices of hyperbolic type are investigated from the integrability viewpoint. More precisely we concentrate on a method for constructing generalized symmetries. This kind integrable…
There are three complete plane geometries of constant curvature: spherical, Euclidean and hyperbolic geometry. We explain how a closed oriented surface can carry a geometry which locally looks like one of these. Focussing on the hyperbolic…
The higher order contact of a quadric with a surface in $3$-space at a non-degenerate point is obtained by the Moutard quadric in the Darboux direction. In this paper, we discuss the extension of this result to hypersurfaces in arbitrary…
$N$-body non efimovian bound or quasi-bound states for particles with short range interactions are considered in arbitrary dimensions. The different resonance regimes near the threshold are depicted by using a generalization of the…
These notes provide an introduction to Giroux's theory of convex surfaces in contact 3-manifolds and its simplest applications. They put a special emphasis on pictures and discussions of explicit examples. The first goal is to explain why…
The chains studied in this paper generalize Chern-Moser chains for CR structures. They form a distinguished family of one dimensional submanifolds in manifolds endowed with a parabolic contact structure. Both the parabolic contact structure…
We introduce the notion of abelian almost contact structures on an odd dimensional real Lie algebra $\mathfrak g$. This a sufficient condition for the structure to be normal. We investigate correspondences with even dimensional real Lie…
There are two well-known parabolic split $G_2$-geometries in dimension five, $(2,3,5)$-distributions and $G_2$-contact structures. Here we link these two geometries with yet another $G_2$-related contact structure, which lives on a…
The theory of $G$-structures provides us with a unified framework for a large class of geometric structures, including symplectic, complex and Riemannian structures, as well as foliations and many others. Surprisingly, contact geometry -…
Previous study of contact of power-law graded materials concerned the contact of a rigid body (punch) with an elastic inhomogeneous foundation whose inhomogeneity is characterized by the Young modulus varying with depth as a power function.…
We find a general solution to the unique 7th order ODE admitting ten dimensional group of contact symmetries. The integral curves of this ODE are rational contact curves in $\PP^3$ which give rise to rational plane curves of degree six. The…
In this article, we use the second intrinsic volume to define a metric on the space of homothetic classes of Gaussian bounded convex bodies in a separable real Hilbert space. Using kernels of hyperbolic type, we can deduce that this space…
A deep relationship [arXiv:2503.17816v1] between real linear second order ordinary differential equations $u''\left(x\right)+h\left(x\right)u\left(x\right)=0$, with differentiable $h(x)$, and two dimensional hyperbolic geometry is…
k-Contact geometry is a generalisation of contact geometry to analyse field theories. We develop an approach to k-contact geometry based on distributions that are distributionally maximally non-integrable and admit, locally, k commuting…
Motivated by the desire of finding a geometric interpretation to the Yamabe equation on groups of Heisenberg type, we define a geometric structure on manifolds modelled locally on these groups, which we call contact structure of Heisenberg…
All second order scalar differential invariants of symplectic hyperbolic and elliptic Monge-Amp\`ere equations with respect to symplectomorphisms are explicitly computed. In particular, it is shown that the number of independent second…
Elie Cartan's general equivalence problem is recast in the language of Lie algebroids. The resulting formalism, being coordinate and model-free, allows for a full geometric interpretation of Cartan's method of equivalence via reduction and…