Science-advisor
REGISTER info/FAQ
Login
username
password
     
forgot password?
register here
 
Research articles
  search articles
  reviews guidelines
  reviews
  articles index
My Pages
my alerts
  my messages
  my reviews
  my favorites
 
 
Stat
Members: 3643
Articles: 2'488'730
Articles rated: 2609

29 March 2024
 
  » arxiv » math.DG/0109178

 Article overview


Projectively Flat Finsler Metrics of Constant Curvature
Zhongmin Shen ;
Date 23 Sep 2001
Subject Differential Geometry; Metric Geometry MSC-class: 53C60; 53B40 | math.DG math.MG
AbstractIt is the Hilbert’s Fourth Problem to characterize the (not-necessarily-reversible) distance functions on a bounded convex domain in R^n such that straight lines are shortest paths. Distance functions induced by a Finsler metric are regarded as smooth ones. Finsler metrics with straight geodesics said to be projective. It is known that the flag curvature of any projective Finsler metric is a scalar function of tangent vectors (the flag curvature must be a constant if it is Riemannian). Thus it is a natural problem to study those of constant curvature. In this paper, we study the Hilbert Fourth Problem in the smooth case. We first give a formula for x-analytic projective Finsler metrics F(x,y) of constant curvature K=c using a power series with coefficients expressed in terms of f(y):=F(0, y), h(y):=(1/2)F(x,y)^{-1}F_{x^k}(0, y)y^k and c. Then, for any given pair {f(y), h(y)} and any constant c, we give an algebraic formula for smooth projective Finsler metrics with constant curvature K=c and F(0, y)=f(y) and F_{x^k}(0, y)y^k=2f(y)h(y). By these formulas, we obtain several special projective Finsler metrics of constant curvature which can be used as models in Finsler geometry.
Source arXiv, math.DG/0109178
Services Forum | Review | PDF | Favorites   
 
Visitor rating: did you like this article? no 1   2   3   4   5   yes

No review found.
 Did you like this article?

This article or document is ...
important:
of broad interest:
readable:
new:
correct:
Global appreciation:

  Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.

browser claudebot






ScienXe.org
» my Online CV
» Free


News, job offers and information for researchers and scientists:
home  |  contact  |  terms of use  |  sitemap
Copyright © 2005-2024 - Scimetrica