Related papers: On Finslerized Absolute Parallelism spaces
The parametric geometry of numbers has allowed to visualize the simultaneous approximation properties of a collection of real numbers through the combined graph of the related successive minima functions. Several inequalities among…
It is shown that four-dimensional generalized symmetric spaces can be naturally equipped with some additional structures defined by means of their curvature operators. As an application, those structures are used to characterize generalized…
The sub-Finslerian geometry means that the metric $F$ is defined only on a given subbundle of the tangent bundle, called a horizontal bundle. In the paper, a version of the Hopf-Rinow theorem is proved in the case of sub-Finslerian…
Lorentz invariance is one of the foundations of modern physics; however, Lorentz violation may happen from the perspective of quantum gravity, and plenty of studies on Lorentz violation have arisen in recent years. As a good tool to explore…
In this paper, we perform a detailed investigation on the various geometrical properties of trapped surfaces and the boundaries of trapped region in general relativity. This treatment extends earlier work on LRS II spacetimes to a general 4…
We relate the novel concept of Topological Data Analysis in Finsler space with representability property, which is a natural obstruction to prevent spurious features in high dimensions. We use decomposition of integer matrix in order to…
Complex Finsler vector bundles have been studied mainly by T. Aikou, who defined complex Finsler structures on holomorphic vector bundles. In this paper, we consider the more general case of a holomorphic Lie algebroid E and we introduce…
In this work, we make new developments in generic cotangent bundle geometries, depending on all phase-space variables. In particular, we will focus on the so-called generalized Hamilton spaces, discussing how the main ingredients of this…
Generalized Berwald manifolds are Finsler manifolds admitting linear connections such that the parallel transports preserve the Finslerian length of tangent vectors (compatibi\-li\-ty condition). By the fundamental result of the theory…
An extension of Riemmann's geometry into a direction dependent geometric structure is usually described by Finsler's geometry. Historically, this construction was motivated by the well-known Riemann's quartic length element example. Quite…
In this article we study convexity properties of distance functions in infinite dimensional Finsler unitary groups, such as the full unitary group, the unitary Schatten perturbations of the identity and unitary groups of finite von Neumann…
Historically, there have been many attempts to produce an appropriate mathematical formalism for modeling the nature of physical space, such as Euclid's geometry, Descartes' system of Cartesian coordinates, the Argand plane, Hamilton's…
In [1] we defined a new kind of space called 'structured space' which locally resembles, near each of its points, some algebraic structure. We noted in the conclusion of the cited paper that the maps $f_s$ and $h$, which are of great…
Generalized coherent states for shape invariant potentials are constructed using an algebraic approach based on supersymmetric quantum mechanics. We show this generalized formalism is able to: a) supply the essential requirements necessary…
A general framework is described which associates geometrical structures to any set of $D$ finite-dimensional hermitian matrices $X^a, \ a=1,...,D$. This framework generalizes and systematizes the well-known examples of fuzzy spaces, and…
Correspondences between k-tuples of points are key in multiple view geometry and motion analysis. Regular transformations are posed by homographies between two projective planes that serves as structural models for images. Such…
The Constraint Satisfaction Problem (CSP) has been intensively studied in many areas of computer science and mathematics. The approach to the CSP based on tools from universal algebra turned out to be the most successful one to study the…
Recently, we have studied the Finsler space with h-Matsumoto change and found Cartan connection for the transformed space [2]. In this paper, we have discussed certain geometrical properties of the hypersurface of a Finsler space for the…
A field theory is constructed in the context of parameterized absolute parallelism geometry. The theory is shown to be a pure gravity one. It is capable of describing the gravitational field and a material distribution in terms of the…
The article presents a new approach to euclidean plane geometry based on projective geometric algebra (PGA). It is designed for anyone with an interest in plane geometry, or who wishes to familiarize themselves with PGA. After a brief…