Related papers: Mechanical Equations on Bi-Para Conformal Geometry

This thesis is focused on some solvable quantum mechanical models and their associated symmetries.

The closure conditions of the inexact exterior differential form and dual form (an equality to zero of differentials of these forms) can be treated as a definition of some differential-geometrical structure. Such a connection discloses the…

Fixed point results with respect to generalized rational contractive mappings in semi-metric spaces endowed with a directed graph are proved. Some examples are provided to illustrate the results. The obtained results extend, improve and…

Recent links between Finsler Geometry and the geometry of spacetimes are briefly revisited, and prospective ideas and results are explained. Special attention is paid to geometric problems with a direct motivation in Relativity and other…

The deformation bicomplex of a module-algebra over a bialgebra is constructed. It is then applied to study algebraic deformations in which both the module structure and the algebra structure are deformed. The cases of module-coalgebras,…

This is a survey on coarse geometry with an emphasis on coarse homology theories.

We discuss and compare several geometric structures which imply an upper bound to the acceleration of a particle measured in its rest system. While all of them have the same implications on the motion of a point particle, they differ in…

We present a geometrical method for analyzing sequential estimating procedures. It is based on the design principle of the second-order efficient sequential estimation provided in Okamoto, Amari and Takeuchi (1991). By introducing a dual…

What is quantum geometry? This question is becoming a popular leitmotiv in theoretical physics and in mathematics. Conformal field theory may catch a glimpse of the right answer. We review global aspects of the geometry of conformal fields,…

In this paper, the geometric properties of the conformal metric are studied and its exact solution of the geodesic deviation equation is presented. We also find out the stress-energy tensor of this geometry and compare it with the usual…

In this paper, conformal motions are studied in plane symmetric static spacetimes. The general solution of conformal Killing equations and the general form of the conformal Killing vector for these spacetimes are presented. All…

We use geometric methods to study two natural two-component generalizations of the periodic Camassa-Holm and Degasperis-Procesi equations. We show that these generalizations can be regarded as geodesic equations on the semidirect product of…

It is demonstrated that, unless the meaning of conformal transformations for the underlying geometrical structure is discussed on a same footing as it is done for the equations of the given gravity theory, the notion of "conformal…

There exist cubical transition systems containing cubes having an arbitrarily large number of faces. A regular transition system is a cubical transition system such that each cube has the good number of faces. The categorical and…

Motivated by recently explored examples, we undertake a systematic study of conformal invariance in one-dimensional sigma models where an isometry group has been gauged. Perhaps surprisingly, we uncover classes of sigma models which are…

An intrinsic definition in terms of conformal capacity is proposed for the conformal type of a Carnot--Carath\'eodory space (parabolic or hyperbolic). Geometric criteria of conformal type are presented. They are closely related to the…

General theory of elliptic hypergeometric series and integrals is outlined. Main attention is paid to the examples obeying properties of the "classical" special functions. In particular, an elliptic analogue of the Gauss hypergeometric…

We review some of the recent work on the dynamics of four dimensional, supersymmetric gauge theories. The kinematics are largely determined by holomorphy and the dynamics are governed by duality. The results shed light on the phases of…

We show that the conformal blocks constructed in the previous article by the first and the third author may be described as certain integrals in equivariant cohomology. When the bundles of conformal blocks have rank one, this construction…

A suite of relational notions of shape are presented at the level of configuration space geometry, with corresponding new theories of shape mechanics and shape statistics. These further generalize two quite well known examples: --1)…