Related papers: Mechanical Equations on Bi-Para Conformal Geometry
The geometry of (2,1) supersymmetric sigma-models is reviewed and the conditions under which they have isometry symmetries are analysed. Certain potentials are constructed that play an important role in the gauging of such symmetries. The…
The parabolic functions are introduced in analogy to the circular and hyperbolic cases. We discuss the relevant properties, the geometrical interpretation and touch on possible generalizations and their link with the modular elliptic…
Meta-conformal transformations are constructed as dynamical symmetries of the linear transport equation in $d$ spatial dimensions. In one and two dimensions, the associated Lie algebras are infinite-dimensional and isomorphic to the direct…
An overview of some recent results on the geometry of partial differential equations in application to integrable systems is given. Lagrangian and Hamiltonian formalism both in the free case (on the space of infinite jets) and with…
In this Thesis we develop the geometric formulations for higher-order autonomous and non-autonomous dynamical systems, and second-order field theories. In all cases, the physical information of the system is given in terms of a Lagrangian…
Application of the noncommutative geometry to several physical models is considered.
We show that there exists an underlying manifold with a conformal metric and compatible connection form, and a metric type Hamiltonian (which we call the geometrical picture) that can be put into correspondence with the usual…
The aim of this paper is to report on recent development on the conformal fractional Laplacian, both from the analytic and geometric points of view, but especially towards the PDE community.
In this work, generalized hypergeometric functions for bicomplex argument is introduced and its convergence criteria is derived. Furthermore, integral representation of this function has been established. Moreover, quadratic transformation,…
The constitutive characterization of the uniformity and homogeneity of binary elastic composites is presented in terms of a combination of the material groupoids of the individual constituents. The incorporation of these two groupoids…
This gives some information about the conformal point and the calibrating conic, and their relationship one to the other. These concepts are useful for visualizing image geometry, and lead to intuitive ways to compute geometry, such as…
This paper can be considered as an extension to our paper [On symplectically harmonic forms on six-dimensional nilmanifolds, Comment. Math. Helv. 76 (2001), n 1, 89-109]. Also, it contains a brief survey of recent results on symplectically…
This paper constructs a Riemann surface associated to the icosahedron and discusses the geodesics associated to a flat metric on this surface. Because of the icosahedral symmetry, this is a distinguished special case of the example treated…
This text is a slightly edited version of lecture notes for a course I gave at ETH, during the Winter term 2000-2001, to undergraduate Mathematics and Physics students. Contents: Chapter 1 - Examples of Dynamical Systems Chapter 2 -…
As a continuation of Rabei et al. work [11], the Hamilton- Jacobi partial differential equation is generalized to be applicable for systems containing fractional derivatives. The Hamilton- Jacobi function in configuration space is obtained…
In this paper, we continue studying the properties of $\gamma$-semi-continuous and $\gamma$-semi-open functions introduced in [5].
This survey article is an invited contribution to the Encyclopedia of Mathematical Physics, 2nd edition. We provide an accessible overview on relevant applications of higher and derived geometry to theoretical physics, including higher…
We review various aspects of two dimensional conformal field theories paying close attention to the algebraic structures that intervene. We provide a compact description regarding the appearance of a chiral algebra as the symmetry algebra…
We propose a conformal generalization of the reversible Vlasov equation of kinetic plasma dynamics, called conformal kinetic theory. In order to arrive at this formalism, we start with the conformal Hamiltonian dynamics of particles and…
This article will appear in the Encyclopedia of Mathematical Physics (Elsevier, 2006).