Related papers: From Vector Analysis to Differential Forms
A natural extension of Riemannian geometry to a much wider context is presented on the basis of the iterated differential form formalism developed in math.DG/0605113 and an application to general relativity is given.
We prove a result on the convex dependence of solutions of ordinary differential equations on an ordered finite-dimensional real vector space with respect to the initial data.
In this paper, we prove a similar result to the fundamental theorem of regular surfaces in classical differential geometry, which extends the classical theorem to the entire class of singular surfaces in Euclidean 3-space known as frontals.…
In this short note, we prove the uniqueness of exterior differentiation on locally finite graphs.
We explicitly describe cohomology of the sheaf of differential forms with poles along a semiample divisor on a complete simplicial toric variety. As an application, we obtain a new vanishing theorem which is an analogue of the…
Eliminating the arbitrary coefficients in the equation of a generic plane curve of order $n$ by computing sufficiently many derivatives, one obtains a differential equation. This is a projective invariant. The first one, corresponding to…
We study non-linear differential equations on the punctured formal disc by considering the natural derived enhancements of their spaces of solutions. In particular, by appealing to results of the inverse theory in the calculus of…
Given an algebra $A$ over a differential field $K$, we study derivations on $A$ that are compatible with the derivation on $K$. There is a universal object, which is a twisted version of the usual module of differentials, and we establish…
The rules of d-separation provide a framework for deriving conditional independence facts from model structure. However, this theory only applies to simple directed graphical models. We introduce relational d-separation, a theory for…
Foundational cases of the generalized Stokes' theorem are visualized using geometric algebra. From considering bivector valued fields, two seldom used instances of the theorem are obtained. Graphical representations are given, showing a…
In this article a sequential theory in the category of spaces and proper maps is described and developed. As a natural extension a sequential theory for exterior spaces and maps is obtained.
This text is the English translation of a 1986 manuscript which gives the classification of the differential forms parametrizing the finite-dimensional Lie algebras of hamiltonian and contact Cartan types over fields of positive…
It is shown that a trivial version of polarization is sufficient to produce separating systems of polynomial invariants: if two points in the direct sum of the $G$--modules $W$ and $m$ copies of $V$ can be separated by polynomial…
In recent literature several derivations of incompressible Navier-Stokes type equations that model the dynamics of an evolving fluidic surface have been presented. These derivations differ in the physical principles used in the modeling…
In this paper after recalling some essential tools concerning the theory of differential forms in the Cartan, Hodge and Clifford bundles over a Riemannian or Riemann-Cartan space or a Lorentzian or Riemann-Cartan spacetime we solve with…
We define vector fields, leaves and trajectories for schemes. With these tools, we are able to give a geometrical interpretation and to generalize several results of differential Galois theory and constructions on differential schemes. We…
It is proved that the set of geodesic circles in two dimensions may be given a variational description and the explicit form of it is presented. In the limit case of the Euclidean geometry a certain claim of uniqueness of such description…
We find the complete equivalence group of a class of (1+1)-dimensional second-order evolution equations, which is infinite-dimensional. The equivariant moving frame methodology is invoked to construct, in the regular case of the…
Differential geometry may be generalized to allow infinitesimals to any order. The purpose of the present contribution is to show that the theory so developed expands received geometrical ideas in an interesting way, rich in potential for…
We give a short proof for the fact that rationality of complex surfaces is a property depending only on the differential structure. Our proof uses the new Seiberg-Witten invariants.