Related papers: Differential $p$-forms and $q$-vector fields with …
We discuss $p$-variation regularity of real-valued functions defined on $[0,T]^2$, based on rectangular increments. When $p>1$, there are two slightly different notions of $p$-variation; both of which are useful in the context of Gaussian…
Gauge $p$-forms in diverse dimensions are ubiquitous in supergravity and string theory. This work reviews novel covariant formulations designed to generate arbitrary interacting duality-invariant or chiral (self-dual) $p$-form theories in…
We consider differential modules over real and p-adic differential fields such that their field of constants is real closed (respectively p-adically closed). Using Deligne's work on Tannakian categories and a result of Serre on Galois…
It is shown that two vectors with coordinates in the finite $q$-element field of characteristic $p$ belong to the same orbit under the natural action of the symmetric group if each of the elementary symmetric polynomials of degree…
We consider a family of vector fields defined in some bounded domain of R^p, and we assume that they satisfy Hormander's rank condition of some step r, and that their coefficients have r-1 continuous derivatives. We extend to this nonsmooth…
A survey of some results and open questions related to the following algebraic invariants of compact complex manifolds, that can be obtained from differential forms: cohomology groups, Chern classes, rational homotopy groups, and higher…
We study a class of discontinuous vector fields brought to our attention by multi-legged animal locomotion. Such vector fields arise not only in biomechanics, but also in robotics, neuroscience, and electrical engineering, to name a few…
The Poincare-Hopf theorem tells us that given a smooth, structurally stable vector field on a surface of genus g, the number of saddles is 2-2g less than the number of sinks and sources. We generalize this result by introducing a more…
Both a general and a diagonal u-invariant for forms of higher degree are defined, generalizing the u-invariant of quadratic forms. Both old and new results on these invariants are collected.
We present a general classification of Hamiltonian multivector fields and of Poisson forms on the extended multiphase space appearing in the geometric formulation of first order classical field theories. This is a prerequisite for computing…
The Dolbeault resolution of the sheaf of holomorphic vector fields $Lie$ on a complex manifold $M$ relates $Lie$ to a sheaf of differential graded Lie algebras, known as the Fr\"olicher-Nijenhuis algebra $g$. We establish - following B. L.…
A survey of some recent and important results which have to do with integrable equations and their relationship with the theory of surfaces is given. Some new results are also presented. The concept of the moving frame is examined, and it…
We try to generalize the Poisson cohomology of a 2-dimensional Poisson manifold to the n-vectors on a n-dimensional manifold. We define several cohomologies and we compute locally some of them, in the case of germs at 0 of n-vectors on a…
The aim of the paper is twofold. Firstly, by using the constant rank level set theorem from differential geometry, we establish sharp upper bounds for the dimensions of the solution sets of polynomial variational inequalities under mild…
The differential geometry of almost Grassmann structures defined on a differentiable manifold of dimension n = pq by a fibration of Segre cones SC (p, q) is studied. The peculiarities in the structure of almost Grassmann structures for the…
One unusual property of dynamic systems, whose state is characterized by a set of scalar dynamic variables satisfying a system of differential equations of a general form, is considered. This property is related to the behavior of equations…
The completeness of the group classification of systems of two linear second-order ordinary differential equations with constant coefficients is delineated in the paper. The new cases extend what has been done in the literature. These cases…
Let $M$ be either a projective manifold $(M,Pi)$ or a pseudo-Riemannian manifold $(M,g).$ We extend, intrinsically, the projective/conformal Schwarzian derivatives that we have introduced recently, to the space of differential operators…
We study regular, static, spherically symmetric solutions of Yang-Mills theories employing higher order invariants of the field strength coupled to gravity in $d$ dimensions. We consider models with only two such invariants characterised by…
In this paper, we characterize arbitrary polynomial vector fields on $S^n$. We establish a necessary and sufficient condition for a degree one vector field on the odd-dimensional sphere $S^{2n-1}$ to be Hamiltonian. Additionally, we…