Related papers: Natural operations on differential forms on contac…
Lagrangian contact supersymmetries (depending on derivatives of arbitrary order) are treated in very general setting. The cohomology of the variational bicomplex on an arbitrary graded manifold and the iterated cohomology of a generic…
The class of ordinary linear constant coefficient differential equations is naturally embedded into a wider class by associating differential equations to algebraic curves.
We give a description of the field of rational natural differential invariants for a class of nonlinear differential operators of order $k\ge 2$ on a smooth manifold of dimension $n\ge 2$ and show their application to the equivalence…
Given a differential operator of geometric origin there exists a list of operations that preserve this property, e.g., tensor products, pull-backs, push-forwards and the middle convolution. We apply certain sequences of these operations to…
Differentiations of operator algebras over non-archimedean spherically complete fields are investigated. Theorems about a differentiation being internal are demonstrated.
In this article, we investigate differential operators on the Siegel-Jacobi space that are invariant under the natural action of the Jacobi group. These invariant differential operators play an important role in the arithmetic theory of…
We give simple characterizations of contact 1-forms in terms of Dirac structures. We also relate normal almost contact structures to the theory of Dirac structures.
In this short note we discuss ordinary differential equations which linearize upon one (or more) differentiations. Although the subject is fairly elementary, equations of this type arise naturally in the context of integrable systems.
In this paper, we consider the locally convex spaces of entire functions with growth given by proximate orders, and study the representation as a differential operator of a continuous homomorphism from such a space to another one. As a…
Given a pair of smooth transversally intersecting manifolds in some ambient manifold, we construct an operator algebra generated by pseudodifferential operators and the (co)boundary operators associated with the submanifolds. We show that…
It is shown that physical fields are formed by physical structures, which in their properties are differential-geometrical structures. These results have been obtained due to using the mathematical apparatus of skew-symmetric differential…
In this note we provide a direct approach to the most basic operator in this theory namely the exterior derivative. The crucial ingredient is a calculus lemma based on determinants. We maintain the view that in a first course at least this…
We develop some basic facts on deformations of exterior differential ideals on a smooth complex algebraic variety. With these tools we study deformations of several types of differential ideals, leading to several irreducible components of…
In this short note, we present certain generalized versions of the commutator formulas of some natural operators on manifolds, and give some applications.
This paper presents a graded hierarchy or chain of binary operations on the reals and the complex numbers. The operations are related distributively in the sense that any one of them distributes over the next lower operation in the chain.…
For a simplicial manifold we construct the differential geometry structure and use it to investigate linear connections, metric and gravity. We discuss and compare three main approaches and calculate the resulting gravity action…
In this work we produce microlocal normal forms for pseudodifferential operators which have a Lagrangian submanifold of radial points. This answers natural questions about such operators and their associated classical dynamics. In a sequel,…
In the theory of species, differential as well as integral operators are known to arise in a natural way. In this paper, we shall prove that they precisely fit together in the algebraic framework of integro-differential rings, which are…
We show how the machine of PROP profiles invented by S. Merkulov can be used to study and classify natural operators in differential geometry. We also give an interpretation of graph complexes arising in this context in terms of…
Results on characterization of manifolds in terms of certain Lie algebras growing on them, especially Lie algebras of differential operators, are reviewed and extended. In particular, we prove that a smooth (real-analytic, Stein) manifold…