Related papers: Differential forms on diffeological spaces and dif…

For every diffeomorphism $\varphi:M\to N$ between 3--dimensional Riemannian manifolds $M$ and $N$ there are in general locally two 2--dimensional distributions $D_{\pm}$ such that $\varphi$ is conformal on both of them. We state necessary…

The shape assumed by a slender elastic structure is a function both of the geometry of the space in which it exists and the forces it experiences. We explore by experiments and theoretical analysis, the morphological phase-space of a…

Flexible slender structures such as rods, ribbons, plates, and shells exhibit extreme nonlinear responses bending, twisting, buckling, wrinkling, and self contact, that defy conventional simulation frameworks. Discrete Differential Geometry…

Here we explore the geometry of the osculating spaces to projective varieties of arbitrary dimension. In particular, we classify varieties having very degenerate higher order osculating spaces and we determine mild conditions for the…

The theories of strings and $D$-branes have motivated the development of non Abelian cohomology techniques in differential geometry, on the purpose to find a geometric interpretation of characteristic classes. The spaces studied here, like…

We investigate the clustering morphology of a swarm of freely rising deformable bubbles. A three-dimensional Vorono\"i analysis enables us to quantitatively distinguish between two typical clustering configurations: preferential clustering…

In this paper higher order mimetic discretizations are introduced which are firmly rooted in the geometry in which the variables are defined. The paper shows how basic constructs in differential geometry have a discrete counterpart in…

This is a note in which we first review symmetries of moduli spaces of stable meromorphic connections on trivial vector bundles over the Riemann sphere, and next discuss symmetries of their integrable deformations as an application. In the…

Motivated by symplectic geometry, we give a detailed account of differential forms and currents on orbifolds with corners, the pull-back and push-forward operations, and their fundamental properties. We work within the formalism where the…

We provide a complete system of invariants for the formal classification of complex analytic unipotent germs of diffeomorphism at $\cn{n}$ fixing the orbits of a regular vector field. We reduce the formal classification problem to solve a…

Within the Hamiltonian formulation of diffeomorphism invariant theories we address the problem of how to determine and how to reduce diffeomorphisms outside the identity component.

Differential forms provide a coordinate-free way to express many quantities and relations in mathematical physics. In particular, they are useful in plasma physics. This tutorial gives a guide so that you can read the plasma physics…

In this article, we study the invariant differential forms which a correspondence of curves admits. We also try to classify the correspondences of $\mathbb{P}^1$ that admits such invariant differential forms.

We consider fibrations of genus 2 over complex surfaces. The purpose of this paper is primarily to provide a geometric description of the possible structures of the fibration on a neighborhood of a singular fiber. In particular it is shown…

For a compact $(2n+1)$-dimensional smooth manifold, let $\mu_M : B Diff_\partial (D^{2n+1}) \to B Diff (M)$ be the map that is defined by extending diffeomorphisms on an embedded disc by the identity. By a classical result of Farrell and…

It is known that the only finite-dimensional diffeological vector space that admits a diffeologically smooth scalar product is the standard space of appropriate dimension. In this note we consider a way to circumnavigate this issue, by…

Systems of ordinary differential equations (or dynamical forms in Lagrangian mechanics), induced by embeddings of smooth fibered manifolds over one-dimensional basis, are considered in the class of variational equations. For a given…

Shells, when confined, can deform in a broad assortment of shapes and patterns, often quite dissimilar to what is produced by their flat counterparts (plates). In this work we discuss the morphological landscape of shells deposited on a…

The aim of this article is to study certain categorical-algebraic frameworks for basic homological algebra, introduced in arXiv:2404.15896, with the aim of better understanding the differences between them. We focus on homological…

We study the problem of conjugating a diffeomorphism of the interval to (positive) powers of itself. Although this is always possible for homeomorphisms, the smooth setting is rather interesting. Besides the obvious obstruction given by…