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Tuesday, November 24, 2020 | History

3 edition of Metric Methods of Finsler Spaces and in the Foundations of Geometry. (AM-8) (Annals of Mathematics Studies) found in the catalog.

Metric Methods of Finsler Spaces and in the Foundations of Geometry. (AM-8) (Annals of Mathematics Studies)

  • 136 Want to read
  • 26 Currently reading

Published by Princeton University Press .
Written in English

    Subjects:
  • Mathematics,
  • Geometry - General,
  • Science/Mathematics,
  • Mathematics / Geometry / General

  • The Physical Object
    FormatPaperback
    Number of Pages243
    ID Numbers
    Open LibraryOL7758297M
    ISBN 10069109571X
    ISBN 109780691095714

      Using Chern's method of transgression, the Euler class of a compact orientable Riemann–Finsler space is represented by polynomials in the connection and curvature matrices of a torsion-free by: 8. A Finsler space is called with -metric if there exists a 2-homogeneous function of two variables such that the Finsler metric is given by where is a Riemannian metric and is a 1-form on. Example 7. (1 0) If, then the Finsler space with Finsler metric is called a Randers by: 1. "Finsler spaces" and "Finsler manifolds" became standard terminology after the publication of Elie Cartan's book Les espaces de Finsler Ⓣ in A Finsler space is a generalisation of a Riemannian space where the length function is defined differently and Minkowski's geometry holds locally. Historical Remarks on Finsler Geometry. Hanno Rund. University of Natal () The fundamental idea of a Finsler space may be traced back to the famous lecture of Riemann:"Uber die Hypothesen, welche der Geometrie zugrnde liegen."In this memoir of Riemann discusses various possibilities by means of which an n-dimensional manifold may be endowed with a metric, and pays particular attention.


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Metric Methods of Finsler Spaces and in the Foundations of Geometry. (AM-8) (Annals of Mathematics Studies) by Herbert Busemann Download PDF EPUB FB2

In no other approach to the foundations of geometry is the idea of a motion as natural and simple as it is in metric spaces; a motion is a mapping of the space on itself which preserves distances.

We establish some simple facts about motions in general metric spaces. The description for this book, Metric Methods of Finsler Spaces and in the Foundations of Geometry. (AM-8), will be forthcoming.5/5(1). The description for this book, Metric Methods of Finsler Spaces and in the Foundations of Geometry.

(AM-8), will be forthcoming. This book provides a wonderful introduction to metric spaces, highly suitable for self-study. The book is logically organized and the exposition is clear.

The pace is leisurely, including ample discussion, complete proofs and a great many examples (so many that I skipped quite a few of them)/5(20).

Busemann, Metric methods in Finsler spaces and in the foundations of geometry, Annals of Mathematics Studies, no. 8, Princeton, Zentralblatt MATH: Mathematical Reviews (MathSciNet): MRCited by: The treatment of metric spaces (Finsler spaces) by the methods of differential geometry involves a lot of geometric objects (tensors, objects of connection etc.), the geometrical background of Which is in most cases not by: 5.

Usually, the methods employed in Finsler geometry involve very complicated tensor computations. Sometimes this discourages beginners. Viewing Finsler spaces as regular metric spaces, the author discusses the problems from the modern metric geometry point of view.

The book begins with the basics on Finsler spaces. Finsler spaces are metric spaces in which the interval between two infinitesimally close points x' and x' + dx' is given by ds -F(xt, dx'), where the Finsler metric function, FMF, F is positively homogeneous of degree one in dxl: F(x', Adx`) = V(x', dxt).Cited by:   Abstract: “Metric geometry” is an approach to geometry based on the notion of length on a topological space.

This approach experienced a very fast development in the last few decades and penetrated into many other mathematical disciplines, such as group theory, dynamical systems, and partial differential equations.

] METRIC FOUNDATIONS OF GEOMETRY. I of general topology apply to metric spaces(7). To indicate this, we recall the following common notions, applying to general metric spaces.

Definition. The sphere of (positive) radius p and center c is the set of all points x satisfying \x — c\ 5¡ p. In the present paper, we introduce the concept of (γ, β)-metric and a number of propositions and theorems have worked for a (γ, β)-metric, where γ3 = aijk(x)yiyjyk is a cubic metric and β.

Finsler geometry and generalizations as an aid in exploring certain less known nonlin. ear aspects and nontrivial symmetries of field equations defined by nonholonomic and. noncommutative structures arising in various models of gravity, classical and quantum.

field theory and geometric by:   Usually, the methods employed in Finsler geometry involve very complicated tensor computations. Sometimes this discourages beginners. Viewing Finsler spaces as regular metric spaces, the author discusses the problems from the modern metric geometry point of view.

The book begins with the basics on Finsler spaces. In Finsler geometry, each point of a base manifold can be endowed with coordinates describing its position as well as a set of one or more vectors describing directions, for example.

The associated metric tensor may generally depend on direction as well as position, and a number of connections emerge associated with various covariant derivatives involving affine and nonlinear by: 9.

The Finsler metric is said to be of class Ck if the restriction of F to the slit tangent bundle TM 0 DTM zero section/is a function of class C k. Note that it is customary in Finsler geometry to require the Finsler metric to be of.

Keywords: Finsler metric, agcurvature, Ricci curvature, Einstein metric, Zermelo navigation, Randers space, Riemannian metric, sectional curvature. Bao’s research was supported in part by R. Uomini and the S.-S. Chern Foundation for Math-ematical Research.

Robles’ research was supported in part by the UBC Graduate Fellowship Program. File Size: KB. Thus Finsler spaces can be viewed as regular metric spaces. Riemannian spaces are special regular metric spaces.

InB. Riemann introduced the Riemann curvature for Riemannian spaces in his ground-breaking Habilitationsvortrag. Thereafter the geometry of these special regular metric spaces is named after : Zhongmin Shen.

New Methods in Finsler Geometry. Pisa, MayAbstracts of presentations. Index of Invited lectures. Title: Duality for Convex Caustics.

Given any metric space, there are several notions of it being negatively curved. In this talk, we single out a weak notion of. FOUNDATIONS OF FINSLER SPACETIMES 5 pointwise concave hypersurface Σ, which becomes then the indicatrix of a Lorentz-Finsler metric L (see Remark ).

This observers’ viewpoint allows one to use geometric methods recently developed in [50] which may have interesting physical applications such as. Abstract. It has become well established in recent years that Finsler geometry can be successfully applied to the study of the physics of relativistic charged particles [1, 2].In particular, a certain new Finsler metric [] has been shown to produce not only the Lorentz equation of motion but also field equations which unify the gravitational and electromagnetic by: 3.

Get this from a library. Metric methods in Finsler spaces and in the foundations of geometry. [Herbert Busemann]. The aim of the book is to expound the geometry of Finsler space regarded as the microlocal space-time of the extended structure of the sub-atomic particles called hadrons.

By generating the quantum field equations in this space, the interactions of hadrons by forming Cited by: 3. The present monograph is motivated by two distinct aims. Firstly, an endeavour has been made to furnish a reasonably comprehensive account of the theory of Finsler spaces based on the methods of classical differential geometry.

Secondly, it is hoped that this monograph may serve also as anBrand: Springer-Verlag Berlin Heidelberg. is determined by a function on the tangent bundle and includes metric geometry. In contrast to the standard formulation of Finsler geometry our Finsler spacetime framework overcomes the differentiability and existence problems of the geometric objects in earlier attempts to use Finsler geometry as an extension of Lorentzian metric geometry.

The present monograph is motivated by two distinct aims. Firstly, an endeavour has been made to furnish a reasonably comprehensive account of the theory of Finsler spaces based on the methods of classical differential : Hanno Rund.

By definition, a Finsler metric on a manifold is a family of Minkowski norms on the tangent spaces. A Minkowski norm on a vector space V is a nonnegative function F: V → [0, +∞) with the.

Definition. A Finsler manifold is a differentiable manifold M together with a Finsler metric, which is a continuous nonnegative function F:TM→[0,+∞) defined on the tangent bundle so that for each point x of M, F(v + w) ≤ F(v) + F(w) for every two vectors v,w tangent to M at x (subadditivity).

F(λv) = λF(v). A Finsler space with a generalized Kropina metric L (a,3) = X32/a is pro jectively flat if and only if' we have () and () and the space is covered by coordinate neighbourhoods in which the Christoffel symbols of the associated Riemannian space with the metric a are written in the form ().Cited by: Finsler space with special Ù, Ú−metric to be Berwald space (Theorem ) and finally, we apply the conformal change of Finsler space with the special Ù, Ú−metric of Douglas type (Theorem ).

a natural framework for the Finsler-Lagrange geometry we develop in this book, while Finsler-Lagrange geometry is presented as a natural framework for applications. This monograph is a natural and necessary continuation of the authors’ work on the theory of Lagrange spaces.

The present volume contains Busemann’s papers on the foundations of geodesic metric spaces and the metric geometry of Finsler spaces. The papers are preceded by a short biography, six essays on various aspects of Busemann’s work, and reviews of two of his books, namely, Metric Methods in Finsler Spaces and in the Foundations of Geometry and The geometry of : Athanase Papadopoulos.

Matsumoto On Finsler space with Randers metric and special forms of importent tensors, J. Math. Kyoto Univ, 14 (), M.

Matsumoto, Foundations of Finsler geometry and special Finsler spaces, Kaiseisha press, Saikawa, Ootsu, Japan, Author: S T Aveesh, S.K. Narasimhamurthy, G.

Ramesh. A metric generalization of Riemannian geometry, where the general definition of the length of a vector is not necessarily given in the form of the square root of a quadratic form as in the Riemannian a generalization was first developed in the paper by P. Finsler. The object studied in Finsler geometry is a real -dimensional differentiable manifold (of class at least) with a.

Finsler geometry naturally appears in the description of various physical systems. In this review, I divide the emergence of Finsler geometry in physics into three categories: dual description of dispersion relations, most general geometric clock and geometry being compatible with the relevant Ehlers–Pirani–Schild by: 6.

Finsler geometry is nota generalization of Riemannian geometry. It is better described as Riemannian geometry without the quadratic re-striction (2). A special case in point is the inter-esting paper [11].

They studied the Kobayashi metric of the domain bounded by File Size: KB. FINSLER GEOMETRY ON COMPLEX VECTOR BUNDLES 85 ruled surface can also be investigated by the study of the Finsler bundle (E;F) (see [Aikou b]). In this article, we shall report on the geometry of complex vector bundles with Finsler metrics, i.e., Finsler bundles.

Let F be a Finsler metric on a holomorphic vector bundle ˇ: E. A space is said to be convex if the unit ball is a convex set. This definition gives the intuition about the convex normed space.

Now I am wondering what would be the similar definition for a. nates do not [Run59]. Let us also point out that in Finsler geometry the unit spheres do not need to be ellipsoids. Finsler geometry is named after Paul Finsler who studied it in his doc-toral thesis in Presently Finsler geometry has found an abundance of applications in both physics and practical applications [KT03, AIM94, Ing96, DC01].File Size: KB.

Jump to Content Jump to Main Navigation. Home About us Subject Areas Contacts About us Subject Areas Contacts. Viewing Finsler spaces as regular metric spaces, this work discusses the problems from the modern metric geometry point of view.

It addresses the basics on Finsler spaces, then deals with basic comparison theorems on metrics and measures and their applications to the Levy concentration theory. Viewing Finsler spaces as regular metric spaces, the author discusses the problems from the modern metric geometry point of view.

The book begins with the basics on Finsler spaces, including the notions of geodesics and curvatures, then deals with basic comparison theorems on metrics and measures and their applications to the Levy concentration.Finsler geometry Finsler geometry has the Finsler complex as the principle question of study this is a differential complex with a Finsler metric, i.e.

a Banach standard characterized on every digression space. A Finsler metric is a significantly more broad structure than a Riemannian metric (M. Matsumoto., ).This collection of works enriches very much the literature on generalized Finsler spaces and opens new ways toward applications by proposing new geometric approaches in gravity, string theory, quantum deformations and noncommutative models.

The book is extremely useful for the researchers in Differential Geometry and Mathematical Physics.