Related papers: Prolongation on Contact Manifolds
We study differential invariants of linear differential operators and use them to find conditions for equivalence of differential operators acting in line bundles over smooth manifolds with respect to groups of authomorphisms.
Motivated by PDE-learning, we give a classifying space for nonlinear operators on simply connected spaces with constant curvature which are also equivariant under the action of the isometry group. The nonlinear operators we are considering…
Contact path geometries are curved geometric structures on a contact manifold comprising smooth families of paths modeled on the family of all isotropic lines in the projectivization of a symplectic vector space. Locally such a structure is…
We give examples of compact symplectic manifolds with disconnected contact type boundary in dimension $4n$ for any $n\geq 1$. The example is given by a subset of the tangent bundle of a compact quotient of the complex hyperbolic space…
Finite plane geometry is associated with finite dimensional Hilbert space. The association allows mapping of q-number Hilbert space observables to the c-number formalism of quantum mechanics in phase space. The mapped entities reflect…
We present simple examples of finite-dimensional connected homogeneous spaces (they are actually topological manifolds) with nonhomogeneous and nonrigid factors. In particular, we give an elementary solution of an old problem in general…
Infinite-dimensional manifolds modelled on arbitrary Hilbert spaces of functions are considered. It is shown that changes in model rather than changes of charts within the same model make coordinate formalisms on finite and…
In this work we consider a class of contact manifolds $(M,\eta)$ with an associated almost contact metric structure $(\phi, \xi, \eta,g)$. This class contains, for example, nearly cosymplectic manifolds and the manifolds in the class…
We consider Dirac operators on odd-dimensional compact spin manifolds which are twisted by a product bundle. We show that the space of connections on the twisting bundle which yield an invertible operator has infinitely many connected…
We consider contact structures on simply-connected 5-manifolds which arise as circle bundles over simply-connected symplectic 4-manifolds and show that invariants from contact homology are related to the divisibility of the canonical class…
Given a contact sub-Riemannian manifold one obtains a non-integrable splitting of the tangent bundle into the directions along the contact distribution and the Reeb field. We generalize the construction of the Bismut superconnection to this…
On the one hand the algebras of linear operators here act on finite-dimensional vector spaces, and on the other hand the point of view is generally an analysts'. Also, one might think of algebras as being used to add more data to basic…
A general formulation of zero curvature connections in a principle bundle is presented and some applications are discussed. It is proved that a related connection based on a prolongation in an associated bundle remains zero curvature as…
Starting from a cubic form, we give a general construction of a quasi-complete homogeneous manifold endowed with a natural contact structure. We show that it can be compactified into a projective contact manifold if and only if the cubic…
In this paper, we study contact structures on any open 3-manifold V which is the interior of a compact 3-manifold. To do this, we introduce proper contact isotopy invariants called the slope at infinity and the division number at infinity.…
The residual finite-dimensionality of a $\mathrm{C}^*$-algebra is known to be encoded in a topological property of its space of representations, stating that finite-dimensional representations should be dense therein. We extend this…
This paper deals with a hyperbolic system of two nonlinear conservation laws, where the phase space contains two contact manifolds. The governing equations are modelling bidisperse suspensions, which consist of two types of small particles…
For operators generated by a certain class of infinite band matrices with matrix elements we establish a characterization of the resolvent set in terms of polynomial solutions of the underlying higher order finite difference equations. This…
We present a Mathai-Quillen interpretation of topological sigma models. The key to the construction is a natural connection in a suitable infinite dimensional vector bundle over the space of maps from a Riemann surface (the world sheet) to…
For semi-Riemannian manifolds of constant sectional curvature, the Calabi operator is a second order linear differential operator that provides local integrability conditions for the range of the Killing operator. In this article, extending…