Related papers: On the completeness of trajectories for some mecha…
We review the canonical theory for perfect fluids, in Eulerian and Lagrangian formulations. The theory is related to a description of extended structures in higher dimensions. Internal symmetry and supersymmetry degrees of freedom are…
The aim of these notes is to discuss the completeness of the dilated systems in a most general framework of an arbitrary sequence lattice $X$, including weighted $\ell^p$ spaces. In particular, general multiplicative and completely…
In spite of its long history and classical character which goes back even to d'Alembert and Lagrange, the problems of constraints in mechanics of continua is still mysterious and full of misunderstandings. Let us mention the problem of…
We lay down the foundations of particle dynamics in mechanical theories that satisfy the relativity principle and whose kinematics can be formulated employing reference frames of the type usually adopted in special relativity. Such…
We give a new scale of completeness conditions for exponential systems in two types of functional spaces on subsets of the complex plane. The first is the Banach spaces of functions that are continuous on a compact and simultaneously…
Our work proposes a unified approach to three different topics in a general Riemannian setting: splitting theorems, symmetry results and overdetermined elliptic problems. By the existence of a stable solution to the semilinear equation…
Motion of a classical particle in 3-dimensional Lobachevsky and Riemann spaces is studied in the presence of an external magnetic field which is analogous to a constant uniform magnetic field in Euclidean space. In both cases three…
Following ideas from a preprint of the second author, see [2], we investigate relations of dynamical Teichmuller spaces with dynamical objects. We also establish some connections with the theory of deformations of inverse limits and…
We develop some aspects of the theory of hyperholomorphic functions whose values are taken in a Banach algebra over a field -- assumed to be the real or the complex numbers -- and which contains the field. Notably, we consider Fueter…
The conformal properties of complex Finsler metrics are studied. We give a characterization of a compact complex Finsler manifold to be globally conformal K\"ahler. The critical points of the total holomorphic curvature and total Ricci…
Projective spaces for finite-dimensional vector spaces over general fields are considered. The geometry of these spaces and the theory of line bundles over these spaces is presented. Particularly, the space of global regular sections of…
The first free comprehensive textbook on quantum (and classical) field theory. The approach is pragmatic, rather than traditional or artistic: It includes practical techniques, such as the 1/N expansion (color ordering) and spacecone…
The space of all Riemannian metrics on a smooth second countable finite dimensional manifold is itself a smooth manifold modeled on the space of symmetric (0,2)-tensor fields with compact support. It carries a canonical Riemannian metric…
Any three-dimensional Riemannian metric can be locally obtained by deforming a constant curvature metric along one direction. The general interest of this result, both in geometry and physics, and related open problems are stressed.
We develop the basics of a theory of almost isometries for spaces endowed with a quasi-metric. The case of non-reversible Finsler (more specifically, Randers) metrics is of particular interest, and it is studied in more detail. The main…
In this article we will discuss a few aspects of the spacetime description of matter and fields. In Section:1 we will discuss the completeness of real numbers in the context of an alternate definition of the straight line as a geometric…
The well-known geometric approach to field theory is based on description of classical fields as sections of fibred manifolds, e.g. bundles with a structure group in gauge theory. In this approach, Lagrangian and Hamiltonian formalisms…
The problem of classifying boundary points of space-time, for example singularities, regular points and points at infinity, is an unexpectedly subtle one. Due to the fact that whether or not two boundary points are identified or even…
We work on a 4-manifold equipped with Lorentzian metric $g$ and consider a volume-preserving diffeomorphism which is the unknown quantity of our mathematical model. The diffeomorphism defines a second Lorentzian metric $h$, the pullback of…
The aim of this work is to study the geometry underlying mechanics and its application to describe autonomous and nonautonomous conservative dynamical systems of different types; as well as dissipative dynamical systems. We use different…