Related papers: One dimensional metrical geometry
We provide a comprehensive overview of metric-affine geometries with spherical symmetry, which may be used in order to solve the field equations for generic gravity theories which employ these geometries as their field variables. We discuss…
Variational analysis presents a unified theory encompassing in particular both smoothness and convexity. In a Euclidean space, convex sets and smooth manifolds both have straightforward local geometry. However, in the most basic hybrid case…
In this paper we introduce generalised Markov numbers and extend the classical Markov theory for the discrete Markov spectrum to the case of generalised Markov numbers. In particular we show recursive properties for these numbers and find…
In this paper, we present a generalization of the Askey-Wilson relations that involves a projective geometry. A projective geometry is defined as follows. Let $h>k\geq 1$ denote integers. Let $\mathbb{F}_{q}$ denote a finite field with $q$…
This present paper has the purpose to find certain physical appications of Lobachevsky geometry and of the algebraic geometry approach in theories with extra dimensions. It has been shown how the periodic properties of the uniformization…
The aim of this paper is to develop on the 1-jet space J^1(R,M^4) the jet Generalized Lagrange Geometry for the rheonomic Chernov metric. The associated gravitational and electromagnetic field models based on the rheonomic Finsler Chernov…
I will discuss results of three different types in geometry and topology. (1) General vanishing and rigidity theorems of elliptic genera proved by using modular forms, Kac-Moody algebras and vertex operator algebras. (2) The computations of…
For any finite point set in $D$-dimensional space equipped with the 1-norm, we present random linear embeddings to $k$-dimensional space, with a new metric, having the following properties. For any pair of points from the point set that are…
The first part of this note contains a review of basic properties of the variety of lines contained in an embedded projective variety and passing through a general point. In particular we provide a detailed proof that for varieties defined…
Formerly the geometry was based on shapes, but since the last centuries this founding mathematical science deals with transformations, projections and mappings. Projective geometry identifies a line with a single point, like the perspective…
The earlier approach is used for description of qubits and geometric phase parameters, the things critical in the area of topological quantum computing. The used tool, Geometric (Clifford) Algebra is the most convenient formalism for that…
We give a relationship that yields an effective geometric way of evaluating mean curvature of surfaces. The approach is reminiscent of the Gauss's contour based evaluation of intrinsic curvature. The presented formula may have a number of…
In this Master of Science Thesis I introduce geometric algebra both from the traditional geometric setting of vector spaces, and also from a more combinatorial view which simplifies common relations and operations. This view enables us to…
This note conducts a comparative study of some approximating properties of the metric projection, generalized projection, and generalized metric projection in uniformly convex and uniformly smooth Banach spaces. We prove that the inverse…
A special class of metrics, called universal metrics, solve all gravity theories defined by covariant field equations purely based on the metric tensor. Since we currently lack the knowledge of what the full of quantum-corrected field…
Several tools have been developed to enhance automation of theorem proving in the 2D plane. However, in 3D, only a few approaches have been studied, and to our knowledge, nothing has been done in higher dimensions. In this paper, we present…
This text is a survey of derived algebraic geometry. It covers a variety of general notions and results from the subject with a view on the recent developments at the interface with deformation quantization.
The scalar fields of supersymmetric models are coordinates of a geometric space. We propose a formulation of supersymmetry that is covariant with respect to reparametrizations of this target space. Employing chiral multiplets as an example,…
In this paper geometry is studied with a novel approach. Every geometrical object is defined as a symbol which satisfies some properties. These symbols are then coded into a class of numbers which are named here as many dots numbers (MDN).…
In pregeometry a metric arises as a composite object at large distances. We investigate if its signature, which distinguishes between time and space, could be a result of the dynamics rather than being built in already in the formulation of…