Related papers: Evolution of Ehresmann's jet theory
Observations of jets from quasars and other types of accreting black hole are briefly summarized. The importance of beaming and $\gamma$-ray observations for understanding the origin of these jets is emphasised. It is argued that both the…
We prove the $L^2$ extension theorem for jets with optimal estimate following the method of Berndtsson-Lempert. For this purpose, following Demailly's construction, we consider Hermitian metrics on jet vector bundles.
Many important features of a field theory, {\it e.g.}, conserved currents, symplectic structures, energy-momentum tensors, {\it etc.}, arise as tensors locally constructed from the fields and their derivatives. Such tensors are naturally…
Geometric formulation of Lagrangian relativistic mechanics in the terms of jets of one-dimensional submanifolds is generalized to Lagrangian theory of submanifolds of arbitrary dimension.
We introduce persistent Betti numbers to characterize topological structure of jets. These topological invariants measure multiplicity and connectivity of jet branches at a given scale threshold, while their persistence records evolution of…
The concept of number and its generalization has played a central role in the development of mathematics over many centuries and many civilizations. Noteworthy milestones in this long and arduous process were the developments of the real…
Contemporary relativity theory is restricted in two points: (1) a use of the Riemannian space-time geometry and (2) a use of inadequate (nonrelativistic) concepts. Reasons of these restrictions are analysed in [1]. Eliminating these…
The fibre bundle formulation of gauge theory is generally accepted. The jet manifold machinery completes this formulation and provides the adequate mathematical description of dynamics of fields represented by sections of fibre bundles.…
Einstein's general theory of relativity is the standard theory of gravity, especially where the needs of astronomy, astrophysics, cosmology and fundamental physics are concerned. As such, this theory is used for many practical purposes…
In this paper we extend the geometric formalism of the Hamilton-Jacobi theory for hamiltonian mechanics to the case of classical field theories in the framework of multisymplectic geometry and Ehresmann connections.
Riemannian geometry is a mathematical field which has been the cornerstone of revolutionary scientific discoveries such as the theory of general relativity. Despite early uses in robot design and recent applications for exploiting data with…
The suppression and modification of high-energy objects, like jets, in heavy-ion collisions provide an important window to access the degrees of freedom of the quark-gluon plasma on different length scales. Despite increasingly precise and…
In this paper we construct the jet geometrical extensions of the KCC-invariants, which characterize a given second-order system of differential equations on the 1-jet space $J^1(R,M)$. A generalized theorem of characterization of our jet…
Modifications of Einstein's theory of gravitation have been extensively considered in the past years, in connection to both cosmology and quantum gravity. Higher-curvature and higher-derivative gravity theories constitute the main examples…
The phenomenology of jets associated with a variety of black hole systems is summarized, emphasizing the constraints imposed on their origin. Models of jet formation are reviewed, focusing in particular on recent ideas concerning MHD…
We define an operation of jets on graphs inspired by the corresponding notion in commutative algebra and algebraic geometry. We examine a few graph theoretic properties and invariants of this construction, including chromatic numbers,…
We establish Thom's jet transversality theorem for regular maps from an affine algebraic manifold to an algebraic manifold satisfying a suitable flexibility condition. It can be considered as the algebraic version of Forstneri\v{c}'s jet…
We consider a maximal extension of the Hilbert-Einstein action and analyze several interesting features of the theory. More specifically, the motion is non-geodesic and takes place in the presence of an extra force. These models could lead…
This paper gives a technically elementary treatment of some aspects of Hamilton-Jacobi theory, especially in relation to the calculus of variations. The second half of the paper describes the application to geometric optics, the…
Einstein's general theory of relativity is the standard theory of gravity, especially where the needs of astronomy, astrophysics, cosmology and fundamental physics are concerned. As such, this theory is used for many practical purposes…